WO2010151738A2 - Piezomagnetoelastic structure for broadband vibration energy harvesting - Google Patents

Abstract

The present invention relates to the field of energy harvesting. More particularly, embodiments of the invention relate to methods, systems, and devices for scavenging vibration- based energy from an ambient vibration source. Specific embodiments of the present invention include an energy harvesting device comprising: a) an elongated ferromagnetic cantilevered beam having a base and an opposing end; b) a plurality of piezoceramic elements operably connected to the base of the beam; c) a first support member for supporting the beam at its base; and d) two permanent magnets disposed on a second support member; wherein the base end of the beam is operably connected to the support member such that the beam is suspended lengthwise from the support member at its base and the opposing end of the beam is free and is disposed a selected distance above and between the magnets; and wherein the piezoceramic elements are operably connected in parallel to each other, such that during operation the beam is capable of scavenging vibrational energy from an external excitation source and the piezoceramic elements are capable of converting the harmonic or random vibrational energy into electrical energy. The piezo-magneto-elastic generator results in a 200% increase in the open- circuit voltage amplitude (hence promising an 800% increase in the power amplitude). The inventive piezo-magneto-elastic generator can be applied for use in piezoelectric energy harvesting, as well as in electromagnetic, electrostatic and magnetostrictive energy harvesting techniques and their hybrid combinations with similar devices.

Description

PIEZQMAGNETQELASTIC STRUCTURE FOR BROADBAND VIBRATION ENERGY HARVESTING

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application relies on the disclosure of and claims the benefit of the filing date of U.S. Provisional Application No. 61/269,662, filed June 26, 2009, the disclosure of which is incorporated by reference herein in its entirety.

STATEMENT OF GOVERNMENT INTEREST

[0002] This work was supported by the U.S. Air Force Office of Scientific Research under MURI FA-9550-06- 1-0326. The U.S. Government has certain rights in the invention.

BACKGROUND OF THE INVENTION Field of the Invention

[0003] The present invention relates to the field of energy harvesting. More particularly, embodiments of the invention relate to methods, systems, and devices for scavenging vibration- based energy from an ambient vibration source. Specific embodiments of the present invention include a piezoelectric power generator comprising: a) an elongated ferromagnetic cantilevered beam suspended lengthwise from a support such that a base of the beam is operably connected to the support and an opposing free end of the beam is disposed a selected distance above and between two permanent magnets; and b) a plurality of piezoceramic elements operably connected to the base of the beam, wherein the piezoceramic elements are operably connected in parallel to each other and operably connected to an electrical load.

Description of the Related Art

[0004] Vibration-based energy harvesting has received great attention over the last decade. Basic transduction mechanisms used for vibration-to-electricity conversion include piezoelectric, electromagnetic, electrostatic and magnetostrictive transductions. See, A. Erturk and D. J. Inman, Smart Materials and Structures 18, 025009 (2009); S. P. Beeby, R. N. Torah, M. J. Tudor, P. Glynne -Jones, T. O'Donnell, C. R. Saha and S. Roy, Journal of Micromechanics and Microengineering 17, 1257 (2007); P. D. Mitcheson, P. Miao, B. H. Stark, E. M. Yeatman, A. S. Holmes and T. C. Green, Sensors and Actuators A 115, 523 (2004); and L. Wang and F. G. Yuan, Smart Materials and Structures 17, 045009 (2008).

[0005] Vibration-based energy harvesting is not limited to mechanical sources of vibration and virtually any excitation source is exploitable for the potential of providing a source for scavenging energy, including noise. See, e.g., CR. Mclnnes, et. al., "Enhanced vibrational energy harvesting using nonlinear stochastic resonance, J. Sound and Vibration," 318 (2008) 655-662; Cottone et. al, "Nonlinear energy harvesting," Physical Review Letters (PRL) of the American Physical Society, 102, 080601( 2009); and Litak et. al, "Magnetopiezoelastic energy harvesting driven by random excitations," American Inst. Physics Applied Physics Letters, 96- 214103-1 (2010), the disclosures of which are incorporated by reference herein in their entireties. [0006] Regardless of the transduction mechanism, a primary issue in vibration-based energy harvesting is that the best performance of a generator is usually limited to excitation at its fundamental resonance frequency. If the applied ambient vibration deviates slightly from the resonance condition then the power out is drastically reduced. Hence a major issue in energy harvesting is to enable broadband energy harvesters.

[0007] Researchers have recently focused on the concept of broadband energy harvesting to solve this issue with different approaches. See, M. S. M. Soliman, E. M. Abdel- Rahman, E. F. El-Saadany and R. R. Mansour, J. of Micromechanics and Microengineering 18, 115021 (2007); and B. Marinkovic and H. Koser, Applied Physics Letters 94, 103505 (2009). [0008] One application where broadband energy harvesting would be helpful is with respect to monitoring the structural health of bridges. Sudden structural failures of large bridge spans, including the Interstate 35W Bridge in Minneapolis and the Chan Tho Bridge in Vietnam, have resulted in tragedy. In the United States alone, about 20 percent of the US interstate bridges have been rated as deficient. Our bridges are in a constant state of decomposition and every year the situation worsens.

[0009] Cost efficient methods for monitoring bridges and detecting bridges susceptible to immediate failure has the potential to increase motorist safety and save lives. Remote sensors embedded within machines, structures, and the environment are currently used to collect information about these systems, which is used for condition-based maintenance. Wireless or "less" wire systems for monitoring and maintaining critical systems, such as bridges, buildings, automobiles, and airplanes are highly desired. In the case of bridges, wireless sensor networks have the potential to enable cost efficient, scalable monitoring systems that could be tailored for each bridge's requirements. Wireless systems have the further advantage of being rapidly deployed due to the elimination of the need for running wires for installation at the site. A disadvantage to such wireless systems is that the batteries used to power the devices must be replaced or recharged periodically, rendering the battery a difficult and costly energy source to maintain under these circumstances. Indeed, with respect to monitoring bridges in particular, battery maintenance is not practical, especially when sensors operated by the batteries are located in areas that are extremely difficult to access. [00010] Harvesting energy from the environment, converting it to electrical energy, and optionally storing the energy to power these systems when needed, is one answer to the battery issue. One way to scavenge energy from the environment is to convert locally-exerted strain and/or vibration energy to electrical energy. For example, a device that collects vibration energy from a bridge as automobiles cross the bridge and then converts that energy to electrical energy to be used for powering remote sensing devices or the communications equipment accompanying such devices would be valuable.

[00011] Although remote sensing systems using vibration-based energy harvesting techniques have the capacity to operate indefinitely, without the need for battery maintenance, such systems currently lack conversion efficiencies required to accomplish this goal. Conventional vibration energy harvesters using piezoelectric materials are typically tuned to the frequencies of the machine or structure to which they are attached. In the case of a bridge, however, where a large range of frequencies will be experienced due to the number and type of vehicles crossing the bridge at any particular moment, tuning is not feasible. Further, if tuned to a particular range of frequencies, such a device will operate inefficiently when frequencies outside the tuned range are received and processed by the device.

[00012] Thus, what is needed is a broadband vibration-based energy harvesting device, which will operate efficiently over a wide range of vibration frequencies.

SUMMARY OF THE INVENTION

[00013] Embodiments of the invention provide a novel broadband vibration energy harvester that results in a substantial increase of the voltage output over a range of excitation frequencies. More particularly, embodiments of the invention provide non-resonant piezo- magneto-elastic energy harvesters.

[00014] The piezomagnetoelastic power generator embodiments can be used in several applications of vibration-based energy harvesting, including defense industry applications, structural health monitoring, and various applications of low power electronics. The main goal in energy harvesting is to remove the battery requirement and therefore to minimize the maintenance costs. The piezomagnetoelastic configuration described in this specification gives three times the voltage output of the conventional cantilever configuration over a range of frequencies (for the same beam length and piezoceramic material). Hence the device promises one order of magnitude larger power for the typical case of varying- frequency and off-resonant excitations, which are more common than resonance excitation, a single harmonic frequency). [00015] Provided in embodiments are energy harvesting devices comprising: a) a PZT bender comprising a cantilevered beam with piezoceramic elements; and b) a plurality of magnets; wherein the beam is disposed a selected distance above and between the magnets, such that the beam is capable of exhibiting a three-equilibrium condition described by electromechanical equations (2) and (3):

[00016] x + 2ζx--x(l -x² )-χv = fcosΩt (2)

[00017] v + λv + κx = 0 (3)

[00018] where v is the dimensionless voltage across the load resistance, χ is the dimensionless piezoelectric coupling term in the mechanical equation, K is the dimensionless piezoelectric coupling term in the electrical circuit equation and λ is the reciprocal of the dimensionless time constant (λ <x Xl R₁C _p where R₁ is the load resistance and C_p is the equivalent capacitance of the piezoceramic layers); and optionally wherein the device is capable of exhibiting a large-amplitude voltage response when subjected to excitation at about resonance frequency and at any off-resonance frequency, which can be any excitation source, including vibrations from seismic activity and/or noise, and whether harmonic or random. Indeed, any of the devices, systems, and methods described in this specification can be used or modified accordingly to accommodate energy harvesting from any vibration source.

[00019] Any device embodiment of the invention can further comprise a weighted cantilevered beam for increasing dynamic flexibility.

[00020] In preferred embodiments, energy harvesting devices can comprise two circular rare earth magnets symmetrically disposed with respect to the cantilevered beam.

[00021] Embodiments of the invention can include devices wherein the piezoceramic elements are operably connected with the beam at its base, are disposed on opposing sides of the beam, and are connected in parallel to each other.

[00022] Additionally included as embodiments of the invention are energy harvesting devices comprising: a) an elongated ferromagnetic cantilevered beam having a base and an opposing end; b) a plurality of piezoceramic elements operably connected to the base of the beam; c) a first support member for supporting the beam at its base; and d) two permanent magnets disposed on a second support member; wherein the base end of the beam is operably connected to the support member such that the beam is suspended lengthwise from the support member at its base and the opposing end of the beam is free and is disposed a selected distance above and between the magnets; and wherein the piezoceramic elements are operably connected in parallel to each other, such that during operation the beam is capable of scavenging vibrational energy from an external excitation source and the piezoceramic elements are capable of converting the vibrational energy into electrical energy; and optionally wherein the device is capable of exhibiting a large-amplitude voltage response when subjected to seismic excitation at about resonance frequency and at any off-resonance frequency. Preferred embodiments employ an external seismic vibration source, but noise excitation can also be used. [00023] Such energy harvesting devices can further comprise a weighted cantilevered beam for increasing dynamic flexibility, and/or symmetrically disposed magnets with respect to the beam, and/or piezoceramic elements disposed on opposing sides of the beam and connected in parallel to each other.

[00024] Systems of the present invention include a system for powering an electrical load comprising: a) a piezo-magneto-elastic power source capable of exhibiting a large-amplitude voltage response when subjected to excitation from an ambient vibration source at about resonance frequency and at any off-resonance frequency; and b) an electrical load operably electrically connected with the power source. The excitation source is preferably harmonic, but can be random as well and from noise, seismic, or any other type of excitation source. [00025] Such systems can be useful for providing power to an electronics device, especially one needing less power to operate than is provided by power output of the power source. In such embodiments, a preferred electrical load is a rechargeable battery. Loads may also include capacitors and trickle charges, to name a few. In the case of rechargeable batteries, in particular, recharging a battery of any device that consumes electrical power would save natural resources if the power for recharging the battery is converted from ambient vibrational energy using a device, system, or method of embodiments of the invention. [00026] Such systems can comprise a piezo-magneto-elastic power source configured comprising: a) an elongated ferromagnetic cantilevered beam having a base and an opposing end; b) a plurality of piezoceramic elements operably connected to the base of the beam; c) a first support member for supporting the beam at its base; and d) two permanent magnets disposed on a second support member; wherein the base end of the beam is operably connected to the support member such that the beam is suspended lengthwise from the support member at its base and the opposing end of the beam is free and is disposed a selected distance above and between the magnets; and wherein the piezoceramic elements are operably connected in parallel to each other, such that during operation the beam is capable of scavenging vibrational energy from an external excitation source (preferred is seismic, but noise excitation is included) and the piezoceramic elements are capable of converting the vibrational energy into electrical energy. [00027] Such systems can alternatively comprise a piezo-magneto-elastic power source configured comprising: a) a PZT bender comprising a cantilevered beam with piezoceramic elements; and b) a plurality of magnets; wherein the beam is disposed a selected distance above and between the magnets, such that the beam is capable of exhibiting a three-equilibrium condition described by electromechanical equations (2) and (3):

[00028] x + 2ζx--x(l -x² )-χv = fcosΩt (2)

[00029] v + λv + κx = 0 (3)

[00030] where v is the dimensionless voltage across the load resistance, χ is the dimensionless piezoelectric coupling term in the mechanical equation, K is the dimensionless piezoelectric coupling term in the electrical circuit equation and λ is the reciprocal of the dimensionless time constant (λ <x Xl R₁C _p where R₁ is the load resistance and C_p is the equivalent capacitance of the piezoceramic layers).

[00031] Further embodiments of the invention include a sensor system comprising: a) a piezo-magneto-elastic power source capable of exhibiting a large-amplitude voltage response when subjected to excitation (e.g., seismic or noise, to name a couple types) from an ambient vibration source at about resonance frequency and at any off-resonance frequency; b) one or more sensors for collecting data (for example, data about a structure, environment, living organism, or anything capable of being monitored for objective information about it, such as temperature, density, humidity, stress from physical forces, etc.), wherein the sensors are operably connected with and electrically powered at least in part by the power source; and c) a computer-readable storage medium for storing the data.

[00032] Methods of the invention include, for example, a method of monitoring integrity of a structure comprising: a) providing electrical power output from a piezo-magneto-elastic power source capable of exhibiting a large-amplitude voltage response when subjected to excitation from an ambient vibration source at about resonance frequency and at any off- resonance frequency; b) electrically powering one or more sensors with the electrical power output to collect data (especially data or information about a structure); and c) storing the data on a computer-readable storage medium. Such methods can include the monitoring of any structure, for example, infrastructure (buildings, bridges, cell towers, etc.), a vehicle (cars, trucks, boats, etc.), or a machine (farm equipment, industrial equipment, commercial manufacturing equipment, etc.). [00033] Methods of the invention can include converting mechanical energy to electrical energy comprising: a) operably connecting a PZT bender to an external source of ambient vibrational energy; b) transferring the vibrational energy from the source to the PZT bender; c) converting the energy to electrical energy with piezoceramic elements of the PZT bender; and d) obtaining a large-amplitude voltage response, when subjected to excitation at about resonance frequency and at any off-resonance frequency. Methods according to the invention can harvest energy from any type of excitation source (e.g., seismic or noise, harmonic or random), as well. [00034] Such methods can specifically comprise a PZT bender configured to comprise: a) a cantilevered beam with piezoceramic elements; and b) a plurality of magnets; wherein the beam is disposed a selected distance above and between the magnets, such that the beam is capable of exhibiting a three-equilibrium condition described by electromechanical equations (2) and (3):

[00035] x + 2ζx--x(\-x² )-χv = fcosΩt (2)

[00036] v + Av + «:JC = O (3)

[00037] where v is the dimensionless voltage across the load resistance, χ is the dimensionless piezoelectric coupling term in the mechanical equation, K is the dimensionless piezoelectric coupling term in the electrical circuit equation and A is the reciprocal of the dimensionless time constant (A <x 1/ R₁C where R₁ is the load resistance and C_p is the equivalent capacitance of the piezoceramic layers).

[00038] Alternatively, such methods can comprise a PZT bender comprising a piezo- magneto-elastic power source configured to comprise: a) an elongated ferromagnetic cantilevered beam having a base and an opposing end; b) a plurality of piezoceramic elements operably connected to the base of the beam; c) a first support member for supporting the beam at its base; and d) two permanent magnets disposed on a second support member; wherein the base end of the beam is operably connected to the support member such that the beam is suspended lengthwise from the support member at its base and the opposing end of the beam is free and is disposed a selected distance above and between the magnets; and wherein the piezoceramic elements are operably connected in parallel to each other, such that during operation the beam is capable of scavenging vibrational energy from an external excitation source and the piezoceramic elements are capable of converting the vibrational energy into electrical energy. [00039] Any device described in this specification is intended to be adapted into any system or method employing the device. Likewise, any method of the invention can comprise any system or device described in this specification. Similarly, any system of the invention can employ any device described herein or employ one or more method steps disclosed herein. In certain applications, device, system, and method embodiments of the invention can be adapted, modified, or combined with one or more features of any other device, system, or method of the invention to accomplish a desired goal.

BRIEF DESCRIPTION OF THE DRAWINGS

[00040] FIG. 1 is a schematic diagram illustrating a magneto-elastic configuration.

[00041] FIG. 2 is a schematic diagram illustrating an embodiment of the piezo-magneto- elastic power generator of the present invention.

[00042] FIG. 3A is a graph showing the theoretical voltage history for chaotic strange attractor motion where jc(O) = 1 , JC(O) = 0 , v(0) = 0 , / = 0.083 . [00043] FIG. 3B is a graph showing the Poincare map on its phase portrait of the theoretical chaotic strange attractor motion shown in FIG. 3 A where x(0) = 1 , i(0) = 0 , v(0) = 0 , Ω = 0.8 , ^ = O-Ol , / = 0.083 , / = 0.05 , *τ = 0.5 , Λ = 0.05 .

[00044] FIG. 3 C is a graph showing the theoretical voltage history for large-amplitude periodic motion due to excitation amplitude where x(0) = 1 , i(0) = 0 , v(0) = 0 , / = 0.115 . [00045] FIG. 3D is a graph showing the theoretical voltage history for large-amplitude periodic motion due to initial conditions where *(0) = 1 , x(Q) = 1 , v(0) = 0 , / = 0.083 . [00046] FIG. 4A is a graph of the velocity vs. displacement phase portraits of piezo- magneto-elastic and piezo-elastic systems (x(0) = 1 , x(0) = 1.2 , v(0) = 0 , / = 0.083 , Ω = 0.8 ). [00047] FIG. 4B is a graph of the velocity vs. voltage phase portraits of piezo-magneto- elastic and piezo-elastic systems ( JC(O) = 1 ,i(0) = 1.2 , v(0) = 0 , / = 0.083 , Ω = 0.8 ). [00048] FIG. 5A is a graph showing the velocity vs. open-circuit voltage phase portraits of piezo-magneto-elastic and piezo-elastic configurations, plotted for Ω = 0.7 . [00049] FIG. 5B is a graph showing the velocity vs. open-circuit voltage phase portraits of piezo-magneto-elastic and piezo-elastic configurations, plotted for Ω = 0.9 . [00050] FIGS. 6A-F are graphs of the three-dimensional voltage vs. velocity phase-space trajectories for the frequency range of Ω = 0.5 -1 ; jt(O) = 1 , Jt(O) = 1.2 , v(0) = 0 , / = 0.083 ). [00051] FIG. 7A is a photograph showing use of an embodiment of a piezomagnetoelastic generator according to the invention in combination with a seismic shaker, accelerometer, and a laser vibrometer. [00052] FIG. 7B is a photograph of a piezomagnetoelastic generator embodiment according to the invention.

[00053] FIG. 7C is a schematic diagram of an exemplary piezomagnetoelastic energy harvester under vertical excitation.

[00054] FIGS. 7D-E are photographs showing an exemplary experimental setup for vertical excitation of a piezomagnetoelastic energy harvester providing a close-up view (FIG. 7D) and an overall view of the setup (FIG. 7E).

[00055] FIG. 7F-H are graphs showing an experimental comparison of the piezomagnetoelastic and the piezoelastic configurations for vertical excitation (for the same acceleration input of 0.5g) at 5.5 Hz (FIG. 7F); 6.5 Hz (FIG. 7G); and 7.5 Hz (FIG. 7H). [00056] FIG. 8 A is a graph of the experimental voltage history exhibiting the strange attractor motion for excitation of 0.5g at 8 Hz.

[00057] FIG. 8B is the Poincare map of the strange attractor motion of FIG. 8A.

[00058] FIG. 9 A is a graph showing experimental voltage history for large-amplitude periodic motion due to the excitation amplitude (excitation: 0.8g at 8 Hz). [00059] FIG. 9B is a graph showing experimental voltage history for large -amplitude periodic motion due to a disturbance at t = 11 s (excitation: 0.5g at 8 Hz). [00060] FIG. 1OA is a graph showing input acceleration histories for piezo-magneto- elastic and piezo-elastic configurations using an excitation of 0.5g at 8 Hz. [00061] FIG. 1OB is a graph showing voltage outputs in the chaotic response region of the piezo-magneto-elastic configuration for excitation of 0.5g at 8 Hz.

[00062] FIG. 1OC is a graph showing voltage outputs in the large-amplitude region of the piezo-magneto-elastic configuration (excitation: 0.5g at 8 Hz).

[00063] FIG. 1 IA is a two-dimensional graph of the electromechanical (velocity vs. open- circuit voltage) phase portraits of the piezo-magneto-elastic and piezo-elastic configurations (excitation: 0.5g at 8 Hz).

[00064] FIG. 1 IB is a three-dimensional graph of the electromechanical (velocity vs. open-circuit voltage) phase portraits of the piezo-magneto-elastic and piezo-elastic configurations (excitation: 0.5g at 8 Hz).

[00065] FIG. 12A is a graph showing that the excitation amplitudes of the piezo-magneto- elastic and the piezo-elastic configurations are similar (with an average RMS value of 0.35g). [00066] FIG. 12B is a graph showing the broadband performance of a piezo-magneto- elastic generator compared with a piezo-elastic configuration. [00067] FIG. 13A is a photograph showing the experimental setup used for investigating the power generation performance of the piezo-magneto-elastic energy harvester. [00068] FIG. 13B is a photograph of an embodiment of a piezo-magneto-elastic system.

[00069] FIG. 13C is a photograph showing a piezo-elastic configuration.

[00070] FIGS. 14A-H are graphs of acceleration input and power output of piezo- magneto-elastic and piezo-elastic configurations at steady state for excitation frequencies of 5 Hz (FIGS. 14A-B); 6 Hz (FIGS. 14C-D); 7 Hz (FIGS. 14E-F); and 8 Hz (FIGS. 14G-H). [00071] FIG. 15 is a graph showing average power output of piezo-magneto-elastic and piezo-elastic energy harvester configurations (RMS acceleration input: 0.35g). [00072] FIG. 16 is a schematic diagram of an exemplary piezomagnetoelastic energy harvester combined to an AC-to-DC converter circuit for battery or capacitor charging. [00073] FIG. 17 is a schematic diagram of an exemplary electrostatic energy harvesting system using the bistable magnetoelastic structure.

[00074] FIG. 18 is a schematic diagram of an exemplary electromagnetic energy harvesting system using the bistable magnetoelastic structure. [00075] FIG. 19 is a schematic diagram of an exemplary magnetostrictive energy harvesting system using the bistable magnetoelastic structure.

DETAILED DESCRIPTION OF VARIOUS EMBODIMENTS OF THE INVENTION

[00076] Reference will now be made in detail to various exemplary embodiments of the invention. The following detailed description is presented for the purpose of describing certain embodiments in detail and is, thus, not to be considered as limiting the invention to the embodiments described.

[00077] FIG. 1 provides a schematic of a well-known magneto-elastic configuration. This configuration was first investigated by Moon and Holmes as a mechanical structure capable of exhibiting strange attractor motions. See, F. C. Moon and P. J. Holmes, Journal of Sound and Vibration 65, 275 (1979).

[00078] The Moon-Holmes device consists of a ferromagnetic cantilevered beam with two permanent magnets located symmetrically near the free end and it is subjected to harmonic base excitation. The bifurcations of the static problem are described by a butterfly catastrophe with a sixth order magneto-elastic potential. Depending on the magnet spacing, the ferromagnetic beam may have five (with three stable), three (with two stable) or one (stable) equilibrium positions. For the case with three equilibrium positions (the bi-stable configuration), the governing lumped-parameter equation of motion has the form of the Duffing equation: [00079] X + 2ζx --x(l -x² ) = f cos Ωt (1)

[00080] where x is the dimensionless tip displacement of the beam in the transverse direction, ζ is the mechanical damping ratio, Ω is the dimensionless excitation frequency,

/ is the dimensionless excitation force due to base acceleration (/ x Ω²X₀ where X₀ is the dimensionless base displacement amplitude) and an over-dot represents differentiation with respect to dimensionless time. The three equilibrium positions obtained from Eq. (1) are (x,i) = (θ, θ) (a saddle) and (x,x) = (±l,θ) (two centers). Detailed nonlinear analysis of the magneto-elastic structure shown in FIG. 1 can be found in Moon-Holmes (1979) mentioned above; and P. Holmes, Philosophical Transactions of the Royal Society A 292, 419 (1979). [00081] The inventors have introduced piezoelectric coupling to this magneto-elastic structure in order to obtain a piezo-magneto-elastic configuration for vibration energy harvesting. Using the device over a range of frequencies, one can generate much larger voltage from the substantially large amplitude oscillations on the high-energy orbits at different frequencies. [00082] FIG. 2 provides a schematic illustrating an embodiment of the present invention which is a bimorph piezo-magneto-elastic power generator 200. More specifically, to use the Moon-Holmes device as a piezoelectric energy harvester, two piezoceramic layers can be attached onto the root of the cantilever to obtain a bimorph generator. [00083] As shown in FIG. 2, this embodiment of the generator 200 comprises a ferromagnetic cantilevered beam 201 with two permanent magnets 202 located symmetrically near the free end of the beam 201, which is subjected to harmonic base excitation. As shown, the beam 201 is suspended from a support member 205 and the magnets are disposed on a second support member 206, which can be integral or separate from support member 205. It is important to note that FIG. 2 is merely a schematic diagram of the piezo-magneto-elastic configuration and is not intended to reflect the actual shape or size of the device. Additionally, a plurality of magnets, eg, two or more, can be used and any type of magnet, including electromagnets can be used. The invention is not limited to the embodiments and specific configurations described herein and appropriate modifications and additions will be apparent to those of skill in the art to adapt the systems and devices of embodiments of the invention to particular applications. The bifurcations of the static problem are described by a butterfly catastrophe with a sixth order magneto-elastic potential. Depending on the spacing of magnets 202, the ferromagnetic beam 201 may have five (with three stable), three (with two stable) or one (stable) equilibrium positions. For the case with three equilibrium positions, the governing lumped-parameter equation of motion has the form of the Duffing equation:

[00084] x + 2ζx--x(l-x² ) = f cosΩt (1)

[00085] where x is the dimensionless tip displacement of the beam in the transverse direction, ζ is the mechanical damping ratio, Ω is the dimensionless excitation frequency,

/ is the dimensionless excitation force due to base acceleration (/ x Q²X₀ where X₀ is the dimensionless base displacement amplitude) and an over-dot represents differentiation with respect to dimensionless time. The three equilibrium positions obtained from Eq. (1) are

(JC,JC) = (O, O) (a saddle) and (JC, JC) = (±1,0) (two centers).

[00086] Further included in the device 200 are two piezoceramic layers 203 attached to the root of the cantilever beam 201, which results in a bimorph generator. The invention is not limited to using only two piezoceramic elements and a plurality of piezoceramic layers 203 can also be used for certain applications. The piezoceramic layers 203 are operably connected to an electrical load 204 (a resistor for simplicity) and the voltage output of the generator 200 across the load 204 due to seismic excitation is the primary interest in energy harvesting. [00087] Taking into account piezoelectric coupling into Eq. (1) and applying the

Kirchhoff laws to the circuit with a resistive load (FIG. 2) leads to the following electromechanical equations:

[00088] x + 2ζx--x(l -x² )-χv = fcosΩt (2)

[00089] v + λv + κx = Q (3)

[00090] where v is the dimensionless voltage across the load resistance, χ is the dimensionless piezoelectric coupling term in the mechanical equation, K is the dimensionless piezoelectric coupling term in the electrical circuit equation and λ is the reciprocal of the dimensionless time constant (λ QC 1/ R₁C where R₁ is the load resistance and C_p is the equivalent capacitance of the piezoceramic layers). Note that the possible nonlinearity coming from piezoelectric coupling is ignored in Equations (2) and (3), assuming the standard form of the linear piezoelectric constitutive relations. See, Erturk and Inman (2009); A. Erturk and D. J. Inman, ASME Journal of Vibration and Acoustics 130, 041002 (2008); and A. Erturk, O. Bilgen and D. J. Inman, Applied Physics Letters 93, 224102 (2008). [00091] The state-space form of Equations (2) and (3) can be expressed as: [00092] χu₃ + /cos Ω? (4)

[00093] where the state variables are M₁ = x , U₂ = x and U₃ = v. The electromechanically coupled equations given by Equation (4) can be used in an ordinary differential equation solver for numerical simulations (the ode45 command of MATLAB is used here).

[00094] FIGS. 3A and 3B are graphs showing time domain simulations of the voltage response for different excitation amplitudes and initial conditions, including for Ω = 0.8 ,

^^" = 0.01 , χ = 0.05 , K = 0.5 and λ = 0.05 (close to open-circuit conditions).

[00095] In the first case, given by FIG. 3A, the forcing term is / = 0.083 and the motion starts with an initial deflection at one of the stable equilibrium positions (x(0) = 1 with zero initial velocity and voltage: i(0) = v(0) = 0 ). The resulting vibratory motion is on a chaotic strange attractor (yielding the chaotic voltage history shown in FIG. 3A) and the Poincare map of this strange attractor motion is shown in FIG. 3 B on its phase portrait.

[00096] FIG. 3 C provides a graph showing that if the excitation amplitude is increased by keeping the same initial conditions, the transient chaotic behavior is followed by large-amplitude oscillations on a high-energy orbit with improved voltage response. FIG. 3D shows that this type of large-amplitude voltage response can be obtained with the original excitation amplitude

(of FIG. 3A) with different initial conditions, simply by imposing an initial velocity condition so that x(0) = l , jc(O) = 1.2 , v(0) = 0 ).

[00097] Having observed the large-amplitude electromechanical response obtained on high-energy orbits of the piezo-magneto-elastic energy harvester configuration described by

Equations (2) and (3), a simple comparison can be made against the conventional piezo-elastic configuration (which is the linear cantilever configuration without the magnets causing the bi- stability). The lumped-parameter equations of the linear piezo-elastic configuration are:

[00098] x + 2^x + x -/v = /cosΩr (5)

[00099] v + λv + κx = 0 (6)

[000100] which can be given in the state-space form as:

[000101] U₁ -2ζu₂ - U₁ + χu₃ + f cos Qt (7)

-Xu₃ - Ku₁ [000102] For the same numerical input (Ω = 0.8 , ζ = 0.01 , χ = 0.05 , K = 0.5 and 1 = 0.05 ), initial conditions and the forcing amplitude of FIG. 3D ( x(0) = 1 , jc(O) = 1.2 , v(0) = 0, / = 0.083 ), one can simulate the voltage response of the piezo-elastic configuration using Equation (7).

[000103] FIG. 4A shows the velocity against displacement phase portrait of the piezo- magneto-elastic and the piezo-elastic configurations. As can be seen from the steady-state orbits appearing in this figure, for the same excitation amplitude, system parameters and the forcing amplitude, the steady-state vibration amplitude of the piezo-magneto-elastic configuration can be much larger than that of the piezo-elastic configuration.

[000104] FIG. 4B shows the velocity against voltage phase portrait of the piezo-magneto- elastic and the piezo-elastic configurations. Expectedly, the large-amplitude response on the high-energy orbit is also observed. For the system parameters used in these simulations and compared in FIGS. 4A-B, the phase between the voltage and the velocity is approximately 90 degrees because the system is close to open-circuit conditions. Therefore, in open-circuit conditions, it is reasonable to plot the velocity against voltage output as the electromechanical phase portrait (as an alternative to the conventional velocity against displacement phase portrait). From the experimental point of view, it is advantageous to plot these two independent measurements (voltage output of the piezoceramic against the velocity signal from the laser vibrometer) rather than integrating the experimental velocity history (as it typically results in a non-uniform drift).

[000105] The superiority of the piezo-magneto-elastic configuration over the piezo-elastic configuration can be shown by plotting these trajectories at several other frequencies except for the resonance (Ω = 1 ) case of the linear problem for which the piezo-elastic configuration generates more voltage. However, at several other frequencies (e.g. Ω = 0.6 , Ω = 0.7 , Ω = 0.9 ), a substantially amplified response similar to the case of Ω = 0.8 can be obtained. [000106] FIG. 5A is a graph showing the velocity vs. open-circuit voltage phase portraits of the piezo-magneto-elastic and the piezo-elastic configurations, plotted for Ω = 0.7 . [000107] FIG. 5B is a graph showing the velocity vs. open-circuit voltage phase portraits of the piezo-magneto-elastic and the piezo-elastic configurations, plotted for Ω = 0.9 . [000108] FIGS. 6A-F are graphs showing the three-dimensional voltage vs. velocity phase- space trajectories for the frequency range of Ω = 0.5 -1 . In all cases, the system parameters, initial conditions and the forcing amplitude are the identical. It should be noted that the forcing amplitude in the base excitation problem is proportional to the square of the frequency (/ oc 0.¹X₀). Keeping the forcing amplitude/constant at different frequencies implies keeping the base acceleration amplitude the same. Hence the base displacement amplitudes are different. [000109] As shown in FIG. 6A, the electrical output of the piezo-magneto-elastic configuration is not considerably larger because the trajectory oscillates around one of its foci. That is, the forcing amplitude cannot overcome the attraction of the magnetic force at the respective focus. As a result, the piezo-magneto-elastic configuration oscillates on a low-energy orbit and its electrical response amplitude is indeed comparable to that of the piezo-elastic configuration. As shown in FIGS. 6B-E, over the frequency range of Ω = 0.6-0.9 , the piezo- magneto-elastic configuration shows a very large amplitude electromechanical response on a high-energy orbit compared to the orbit of the piezo-elastic configuration. Note that the response amplitude of the piezo-elastic configuration grows as one moves close to the resonance (Ω ≥ 1 ) of the piezo-elastic configuration. Yet the piezo-magneto-elastic configuration generates dramatically larger steady-state voltage output in this frequency range (Ω = 0.6 - 0.9 ). [000110] As shown in FIG. 6F, expectedly at Ω = 1 , the response amplitude of the piezo- elastic configuration is larger. It is worth adding that, at this particular frequency where the resonant configuration generates more voltage, the difference in the response amplitudes is not as dramatic as at other frequencies where the non-resonant configuration is much superior. [000111] Experimental verifications of the concept (i.e., the presence of these high-energy orbits to utilize for piezoelectric energy harvesting) are given in the following sections. [000112] FIGS. 7A and 7B show the piezo-magneto-elastic energy harvester 700 and corresponding experimental setup used in the experiments. As shown in FIG. 7A, harmonic base excitation is provided by a seismic shaker 710 (Acoustic Power Systems APS-113) and the velocity response of cantilever 701 is recorded by a laser vibrometer 730 (Polytec OFV303 laser head with OFV3001 vibrometer). As shown in FIG. 7B, acceleration at the base of cantilever 701 is measured by a small accelerometer 720 (PCB Piezotronics Model U352C67). The time history of the base acceleration, voltage, and vibration responses are recorded by a National Instruments NI cDAQ-9172 data acquisition system (with a sampling frequency of 2000 Hz). The ferromagnetic beam 701 (made of tempered blue steel) is 145 mm long (overhang length), 26 mm wide and 0.26 mm thick. A lumped mass of 14 grams is attached close to the tip for improved dynamic flexibility.

[000113] Two PZT-5A piezoceramic layers 703 (QP16N, Mide Corporation) are attached onto both faces of the beam 701 at the root using a high shear strength epoxy and they are connected in parallel. The spacing between the symmetrically located circular rare earth magnets 702 is 50 mm (center to center) and this distance is selected to realize the three equilibrium case described by Equations (2) and (3) described above. The tip deflection of the magnetically buckled beam 701 in the static case to either side is approximately 15 mm relative to the unstable equilibrium position (x = 0 ). The post-buckled fundamental resonance frequency of the beam is 10.6 Hz (at both focus points) whereas the fundamental resonance frequency of the unbuckled beam (when the magnets are removed) is 7.4 Hz (both under the open-circuit conditions of piezoceramics - i.e. at constant electric displacement). [000114] It is important to note that, in practice, often the direction of vibratory motion is vertical as depicted in FIG. 7C. With vertical excitation, gravity acts on the harvester beam in an uneven way compared to horizontal excitation. In other words, in the absence of the tip magnets, the static equilibrium of the flexible beam is biased towards the ground. Therefore, the lower magnet should be moved downwards to create equal magnetic forces at the tip as shown in FIGS. 7D-E (close-up view and full set up view). Once this adjustment is made, the same broadband phenomenon is observed for the piezomagnetoelastic energy harvester configuration as shown in FIG. 7F-H (with comparisons against the piezoelastic configuration). [000115] FIG. 8A shows the chaotic open-circuit voltage response obtained for a harmonic excitation amplitude of 0.5g (where g is the gravitational acceleration: g = 9.81 m/s ) at 8 Hz, with an initial deflection at one of the stable equilibrium positions (15 mm to the shaker side), and zero initial velocity and voltage. FIG. 8B shows the Poincare map of the strange attractor motion of FIG. 8A. These figures are obtained from a measurement taken for about 15 minutes (1,784,400 data points due to a sampling frequency of 2000 Hz) and they exhibit very good qualitative agreement with the theoretical strange attractor given by FIGS. 3A-B. [000116] As shown in FIG. 9A, if the excitation amplitude is increased to 0.8g (at the same frequency), the structure goes from transient chaos to a large-amplitude periodic (limit cycle) motion with a strong improvement in the voltage response. A similar improvement is obtained in FIG. 9B where the excitation amplitude is kept as the original one (0.5g) and a disturbance (hand impulse) is applied at t = 11 s (as a simple alternative to creating a velocity initial condition). Such a disturbance can be realized in practice by applying an impulse type voltage input through one of the piezoceramic layers for an instant. The experimental evidence given with FIGS. 9A-B is in agreement with the theoretical discussion given with FIGS. 3C-D. [000117] Noticing the large-amplitude steady-state voltage response obtained at an off- resonance frequency in FIGS. 9A-B, the broadband performance of the device is investigated and comparisons against the piezo-elastic configuration are given in the next section. [000118] Broadband Voltage Generation.

[000119] Comparisons of the piezo-magneto-elastic and piezo-elastic configurations were made. For purposes of the comparison, the piezo-elastic configuration was obtained by removing the magnets of the piezo-magneto-elastic configuration. Before a comparison of these configurations is given over a frequency range, reconsideration of the voltage history of FIG. 9B should be considered in two parts. The time history until the instant of the disturbance is chaotic, which would yield a strange attractor motion similar to what was shown in FIGS. 8A-B if no disturbance was applied. After the disturbance is applied at t = l l s, the large-amplitude response on a high-energy orbit is obtained as the steady-state response. [000120] In order to understand the advantage of the second region in the response history of FIG. 9B, the open-circuit voltage histories of the piezo-magneto-elastic and piezo-elastic configurations are compared for the same harmonic input (0.5g at 8 Hz). [000121] FIGS. lOA-C provide a comparison of the input and the output time histories of the piezo-magneto-elastic and piezo-elastic configurations, namely FIG. 1OA shows input acceleration histories; FIG. 1OB shows voltage outputs in the chaotic response region of the piezo-magneto-elastic configuration; and FIG. 1OC shows voltage outputs in the large-amplitude region of the piezo-magneto-elastic configuration (excitation: 0.5g at 8 Hz). [000122] More particularly, FIG. 1OA shows the acceleration input to the piezo-magneto- elastic and the piezo-elastic configurations at an arbitrary instant of time. The voltage input to the seismic shaker is identical for both configurations, yielding very similar base acceleration amplitudes (according to the signal output of the accelerometer) for a fair comparison. [000123] FIG. 1OB displays the comparison of the piezo-magneto-elastic and the piezo- elastic configurations where the former exhibits chaotic response and the latter has already reached its harmonic steady-state response amplitude at the input frequency. As a rough comparison, from FIG. 1OB, it is not possible to claim that the chaotic response of the piezo- magneto-elastic configuration has any advantage over the harmonic response of the piezo-elastic configuration as their amplitudes look very similar (a more accurate comparison can be made through the RMS -root mean square - amplitudes). Besides, one would definitely prefer a periodic signal to a chaotic signal when it comes to processing the harvested energy using an efficient energy harvesting circuit.

[000124] FIG. 1OC shows the voltage histories of these configurations some time after the disturbance is applied to the piezo-magneto-elastic configuration and the large-amplitude response is obtained. Obviously if the same disturbance is applied to the piezo-elastic configuration, the trajectory (in the phase space) returns to the same low-amplitude orbit after some transients. Therefore the response amplitude of the piezo-elastic configuration is identical in FIGS. 1OB and 1OC. Although the chaotic response of the piezo-magneto-elastic structure has no considerable advantage according to FIG. 1OB, the large -amplitude response of this structure can give more than 3 times larger RMS voltage output according to FIG. 1OC. [000125] Larger power output from the systems and devices could be expected when using noise as the excitation source. See Cottone et al, PRL 2009 above (which describes a bistable configuration giving larger power output to noise excitation.

[000126] FIG. 1 IA compares the velocity vs. voltage phase portraits of the piezo-magneto- elastic and piezo-elastic configurations for excitation at 8 Hz with 0.5g, showing the advantage of the large-amplitude orbit clearly. This figure is therefore analogous to the theoretical demonstration given by FIG. 4B (additional harmonics are present in the experimental data of the distributed-parameter piezo-magneto-elastic structure).

[000127] FIG. 1 IB shows the three-dimensional view of the electromechanical trajectory in the phase space, which shows good qualitative agreement with its simplified theoretical counterpart based on the lumped-parameter model (FIGS. 6A-F). Comparisons using different frequencies to see if similar high-energy orbits can be reached at other frequencies as well (as in the theoretical case) are discussed next.

[000128] For a harmonic base excitation amplitude of 0.5g (yielding an RMS acceleration of 0.35g), experiments are conducted at 4.5 Hz, 5 Hz, 5.5 Hz, 6 Hz, 6.5 Hz, 7 Hz, 7.5 Hz and 8 Hz. As used herein, the term "broadband" refers to a range of frequencies in which the devices, systems, and methods of the invention will operate efficiently, meaning that large- amplitude voltage responses can be experienced regardless of the frequency of the vibrational energy source. For example, the devices, systems, and methods are capable of generating substantial power output regardless of whether the frequency of the vibrational energy is a resonant or non-resonant frequency. At each frequency, a large-amplitude periodic response is obtained the same way as in FIG. 5C with a disturbance around ^ = I I s. Then the magnets are removed for comparison of the device performance with that of the conventional piezo-elastic configuration and the base excitation tests are repeated for the same frequencies with approximately the same input acceleration. The open-circuit RMS voltage outputs of the piezo- magneto-elastic and piezo-elastic configurations at each frequency are obtained considering the steady-state response in the 8Os-IOOs time interval. The RMS values of the input base acceleration are also extracted for the same time interval. [000129] FIG. 12A shows that the excitation amplitudes of both configurations are very similar (with an average RMS value of approximately 0.35g). FIG. 12B shows the broadband performance of the piezo-magneto-elastic generator. The resonant piezo-elastic device gives larger voltage output only when the excitation frequency is at or very close to its resonance frequency (7.4 Hz) whereas the voltage output of the piezo-magneto-elastic device can be 3 times that of the piezo-elastic device at several other frequencies below its post-buckled resonance frequency (10.6 Hz). It should be noted that power output is proportional to the square of the voltage. Hence an order of magnitude larger power output over a frequency range can be expected with this device.

[000130] After the first set of experiments, another setup was prepared to compare the power generation performance of the piezo-magneto-elastic configuration with that of the piezo- elastic configuration to verify the order of magnitude increase in the power output. This section also aims to investigate whether or not the presence of a resistive load (which is known to create shunt damping effect) considerably reduces the performance of the piezo-magneto-elastic configuration by modifying the attraction of the high-energy orbit discussed here. [000131] FIG. 13A shows the experimental setup used for this purpose, which is similar to the set up shown in FIG. 7A. These experiments have been conducted two months after the previous ones and the cantilever was undamped and the magnets were removed in between (which is usually undesired). Therefore, effort has been made to clamp the beam with the same overhang length and to relocate the magnets in a similar way to stay in the same frequency range. As shown in FIG. 13 A, a piezo-magneto-elastic energy harvesting device 1300 is operably connected with a seismic excitation source, here a seismic shaker 1310. The seismic excitation source is used in the experiments herein as a substitute for an external source of vibration or strain. For example, upon installation of a piezo-magneto-elastic device according to the invention on a bridge, for example, the external source of vibration would be caused by vehicular traffic over the bridge and/or environmental conditions to which the bridge is subjected, such as wind, snow, ice, or rain. The piezo-magneto-elastic device can be scaled in size according to a particular application in which it is needed, such as made smaller for installation on automobiles or aircraft instead of buildings or other structures. The device 1300 can be placed on, secured to, or otherwise operably connected with a structure capable of experiencing an external source of vibration, such that the vibration from the structure is transferred to device 1300.

[000132] FIGS. 13B and C, respectively, display the piezo-magneto-elastic device 1300 and the piezo-elastic configuration tested for power generation under base excitation. As shown in FIG. 13B, device 1300 comprises a) an elongated ferromagnetic cantilevered beam 1301 having a base 1308 and an opposing end 1309; b) a plurality of piezoceramic elements 1303 (here, two) operably connected to the base of the beam (here, affixed to opposing sides of the beam); c) a first support member 1305 for supporting the beam 1301 at its base 1308; and d) two permanent magnets 1302 disposed on a second support member 1306; wherein base end 1308 of beam 1301 is operably connected to the support member 1305 such that the beam 1301 is suspended lengthwise from the support member 1305 at its base 1308 and opposing end 1309 of the beam 1301 is free and is disposed a selected distance above and between the magnets 1302; and wherein the piezoceramic elements 1303 are operably connected in parallel to each other, such that during operation the beam 1301 is capable of scavenging vibrational energy from an external seismic excitation source (here, a seismic shaker) and the piezoceramic elements 1303 are capable of converting the vibrational energy into electrical energy. Optionally, mass 1307 can be added to the beam 1301 to improve dynamic flexibility of the system. As shown, the piezoceramic elements 1303 are operably coupled with wires and an electrical load (resistor) for measuring the voltage output of the system. In practice, the load can be any device using electricity to operate and/or a rechargeable battery for such a device. For comparison purposes, FIG. 13C provides a configuration of a piezo-elastic system, which differs from the embodiment of the piezo-magneto-elastic system of FIG. 13B in that the magnets 1302 are removed. [000133] An equally applicable description of the device/system includes describing the device as an energy harvesting device comprising: a) a PZT bender comprising a cantilevered beam with piezoceramic elements; and b) a plurality of magnets; wherein the beam is disposed a selected distance above and between the magnets, such that the beam is capable of exhibiting a three-equilibrium condition described by electromechanical equations (2) and (3):

[000134] x + 2ζx--x[l-x² )-χv ^ fcosΩt (2)

[000135] v + λv + κx = 0 (3)

[000136] where v is the dimensionless voltage across the load resistance, χ is the dimensionless piezoelectric coupling term in the mechanical equation, K is the dimensionless piezoelectric coupling term in the electrical circuit equation and λ is the reciprocal of the dimensionless time constant (λ <x 1/ R₁C where R₁ is the load resistance and C_p is the equivalent capacitance of the piezoceramic layers); and wherein the device is capable of exhibiting a large-amplitude voltage response when subjected to seismic excitation at about resonance frequency and at off-resonance frequencies. The set up of the piezo-magneto-elastic system provided in FIG. 13B is configured to provide such a three-equilibrium condition. Other configurations are also possible depending on the desired effect. [000137] A harmonic base excitation amplitude of 0.5g (yielding an RMS value of approximately 0.35g) is applied at frequencies of 5 Hz, 6 Hz, 7 Hz and 8 Hz. From the previous discussion related to the open-circuit voltage output given with FIG. 12B, it is expected to obtain an order of magnitude larger power with the piezo-magneto-elastic device at three of these frequencies (5 Hz, 6 Hz and 8 Hz). However, it is anticipated to obtain larger power from the piezo-elastic configuration around its resonance and 7 Hz is close to the resonance frequency of this linear system (as can be noted from FIG. 12B).

[000138] FIGS. 14A-H shows the comparison of the average steady-state power vs. load resistance graphs of the piezo-magneto-elastic and piezo-elastic configurations at the frequencies of interest. Note that the excitation amplitudes (i.e., the base acceleration) of both configurations are very similar in all cases. As anticipated, the piezo-magneto-elastic energy harvester gives an order of magnitude larger power at 5 Hz, 6 Hz and 8 Hz whereas the piezo- elastic configuration gives larger power only at 7 Hz (by a factor of 2.3). The average power outputs read from these graphs for the optimum values of load resistance are listed in Table 1.

[000139] Table 1

[000140] Average Power Outputs of the Energy Harvester Configurations

[000141] FIG. 15 shows the variation of the average electrical power outputs of both configurations with the excitation frequency (including the frequencies 5.5 Hz, 6.5 Hz and 7.5 Hz). It is important to notice in FIG. 15 that, at several frequencies, the non-resonant piezo- magneto-elastic energy harvester can indeed generate one order of magnitude more power for the same input. The resonant piezo-elastic energy harvester can generate larger power only within a narrow band around its fundamental resonance frequency. However, this power is not an order of magnitude larger than that of the piezo-magneto-elastic configuration (in qualitative agreement with FIGS. 6A-F).

[000142] From FIG. 15, it can be concluded that the piezo-magneto-elastic configuration exhibits a much better broadband power generation performance provided that the input excitation results in oscillations on its high-energy orbits in the frequency range of interest. Given the frequency range and the amplitude of harmonic base excitation at these frequencies, the piezo-magneto-elastic energy harvester should be designed to catch these high-energy orbits at steady state.

[000143] It is important to note that the devices, systems, and methods according to the invention are equally applicable when coupled with any excitation source. Although seismic vibrational excitation is discussed in detail in the examples provided above, embodiments of the invention include energy harvesting from any excitation source. For example, noise excitation (particularly, stationary Gaussian white noise) provides an alternative vibration source due to stochastic resonance. In simplest terms, such resonance is a nonlinear resonance that occurs in bistable systems when they are excited by noise, and if the noise level reaches a certain threshold. This phenomenon does not happen in monostable systems under noise excitation (such as simple cantilevers without any magnet). Embodiments of the inventive devices have been investigated by others concerning noise-based applications. See Litak (2010) above. [000144] Even further, other various energy harvesting circuits available in the literature can be used with the piezomagnetoelastic energy harvester proposed here. See, e.g., Ottman, G. K., Hofmann, H. F., Bhatt, A. C, and Lesieutre, G. A., Adaptive piezoelectric energy harvesting circuit for wireless remote power supply, IEEE Transactions on Power Electronics, 17:669-676 (2002); Guyomar, D., Badel, A., Lefeuvre, E., and Richard, C, Toward energy harvesting using active materials and conversion improvement by nonlinear processing, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 52:584-595 (2005); Shu, Y. C, Lien, I. C, and Wu, W. J., An improved analysis of the SSHI interface in piezoelectric energy harvesting, Smart Materials and Structures, 16:2253-2264 (2007); and Kong, N., Ha, D.S., Erturk, A., and Inman, DJ., Resistive impedance matching circuit for piezoelectric energy harvesting, J. of MeIl. Material Systems and Structures, 21 (in press, 2010) doi: 10.1177/1045389X09357971. [000145] For example, in piezoelectric energy harvesting, it is often required to use an AC-to-DC converter (rectifier with a smoothing capacitor) and then a DC-to-DC regulator (to adjust the DC voltage level) before the electrical output of the energy harvester can be used for charging a battery or a capacitor, such as is provided in FIG. 16. The broadband power generation (under harmonic excitation) and the stochastic resonance (under noise excitation) features of the piezomagnetoelastic energy harvester can be implemented to other transduction mechanisms and the conclusions drawn for piezoelectric energy harvesting are also valid for electrostatic, electromagnetic and magnetostrictive energy harvesting.

[000146] FIG. 17 describes the use of the bistable magnetoelastic structure for electrostatic energy harvesting using the switching circuit referred from Roundy, S., Wright, P. and Rabaey,

J., A study of low level vibrations as a power source for wireless sensor nodes, Computer Communications, 26: 1131-1144 (2003). In this simple implementation, electrically isolated capacitor fingers are located on the faces of the elastic beam and they oscillate as the elastic beam vibrates in response to base excitation (harmonic or noise excitation). In electrostatic energy harvesting, the vibratory motion of the structure (yielding a relative motion between the capacitor fingers) results in work done against the electrostatic forces between the capacitor fingers, which provides the harvested energy. Unlike in piezoelectric energy harvesting, a voltage input is required in electrostatic energy harvesting. Broadband large-amplitude limit cycles (under harmonic excitation) and stochastic resonance (under noise excitation) of the bistable magnetoelastic configuration shown in FIG. 17 can improve the power output dramatically compared to the conventional configurations. See Beeby, S. P., Tudor, M. J. and White, N. M., Energy harvesting vibration sources for microsystems applications Measurement Science and Technolog}', 13:R175-R195 (review article) (2006). The design can be used both for charge-constrained and voltage-constrained electrostatic energy harvesting. See Beeby 2006. [000147] FIG. 18 shows one way of implementing the magnetoelastic structure for electromagnetic energy harvesting. More particularly, induction of electromagnetic power requires a relative motion between a magnet and a coil due to Faraday's law (e.g. moving magnet and stationary coil or moving coil and stationary magnet). See Glynne- Jones, P., Tudor, M. J., Beeby, S. P. and White, N. M., An electromagnetic, vibration-powered generator for intelligent sensor systems, Sensors and Actuators, A 110:344-349 (2004). The configuration shown in the FIG. 18 considers a moving coil cutting the magnetic field lines of the stationary magnets, yielding an alternating current output, which can then be rectified and regulated to charge a battery or a capacitor. More magnets can be included provided that they do not distort the magnetic field causing the bistability of the beam. The electromagnetic power output is proportional to the relative velocity between the coil and the magnet. See Beeby 2006 above. Since the magnetoelastic configuration results in much larger vibration amplitudes (hence velocity amplitudes) than the conventional cantilever designs, it can improve the electrical power by an order of magnitude over a range of frequencies under harmonic excitation. As in the piezoelectric energy harvesting case, noise excitation can create stochastic resonance when it exceeds a certain level.

[000148] Magnetostrictive materials (e.g. Terfenol-D) deform when placed in a magnetic field and conversely they can induce changes in a magnetic field if strained mechanically. See Beeby 2006 above. A magnetostrictive material with a bias magnetic field can be located at the root of the cantilever (FIG. 19) and the large dynamic strain induced in the magnetostrictive layers under broadband harmonic excitation as well as noise excitation of the magnetoelastic configuration described herein can improve the power output considerably compared to conventional cantilevers used for magnetostrictive energy harvesting. See Wang, L. and Yuan, F. G., Vibration energy harvesting by magnetostrictive material, Smart Materials and Structures, 17:045009 (2008).

[000149] A non-resonant piezo-magneto-elastic energy harvester is introduced for broadband vibration energy harvesting. The magneto-elastic configuration is known from the literature of chaos theory in structural mechanics. The inventors have introduced piezoelectric coupling to the known structure and a piezo-magneto-elastic vibration energy harvester is obtained. The lumped-parameter electromechanical equations describing the nonlinear system are given along with theoretical simulations. The existence of high-energy orbits at different frequencies is demonstrated. It is shown that, over a range of frequencies, one can obtain much larger voltage from the large amplitude oscillations on these orbits (compared to the conventional piezo-elastic configuration). An experimental prototype is built and the presence of such high-energy orbits at several frequencies below the post-buckled natural frequency of the structure is verified. It is shown experimentally that, the open-circuit voltage output of the piezo-magneto-elastic energy harvester can be three times that of the conventional piezo-elastic cantilever configuration, yielding an order of magnitude larger power output over a range of frequencies (for the same base acceleration input). The substantial broadband power generation performance of the magneto-elastic configuration is discussed here for piezoelectric energy harvesting and it can easily be extended to electromagnetic, electrostatic and magnetostrictive energy harvesting techniques as well as to their hybrid combinations. [000150] As described, embodiments of the invention provide a piezo-magneto-elastic generator, which results in a 200% increase in the open-circuit voltage amplitude (hence promising an 800% increase in the power amplitude). Although the experimental performance of the concept is demonstrated in this specification for piezoelectric energy harvesting, this technology can easily be applied to electromagnetic, electrostatic and magnetostrictive energy harvesting techniques as well as to their hybrid combinations with similar devices. The energy harvesting concepts and techniques disclosed in this specification are equally applicable to other applications, including bridge structural health monitoring. [000151 ] The present invention has been described with reference to particular embodiments having various features. It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the scope or spirit of the invention. One skilled in the art will recognize that these features may be used singularly or in any combination based on the requirements and specifications of a given application or design. Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention. The description of the invention provided is merely exemplary in nature and, thus, variations that do not depart from the essence of the invention are intended to be within the scope of the invention.

Claims

1. An energy harvesting device comprising: a PZT bender comprising a cantilevered beam with piezoceramic elements; and a plurality of magnets; wherein the beam is disposed a selected distance above and between the magnets, such that the beam is capable of exhibiting a three-equilibrium condition described by electromechanical equations (2) and (3):

x + 2ζx--x(\-x² )-χv = fcosΩt (2)

v + λv + κx = 0 (3) where v is the dimensionless voltage across the load resistance, χ is the dimensionless piezoelectric coupling term in the mechanical equation, K is the dimensionless piezoelectric coupling term in the electrical circuit equation and λ is the reciprocal of the dimensionless time constant (λ <x 1 / R₁C _p where R₁ is the load resistance and C_p is the equivalent capacitance of the piezoceramic layers); and wherein the device is capable of exhibiting a large -amplitude voltage response when subjected to excitation at about resonance frequency and at any off-resonance frequency.

2. The device of claim 1 further comprising a weighted cantilevered beam for increasing dynamic flexibility.

3. The device of claim 1, wherein the magnets are two circular rare earth magnets symmetrically disposed with respect to the beam.

4. The device of claim 1, wherein the piezoceramic elements are operably connected with the beam at its base, are disposed on opposing sides of the beam, and are connected in parallel to each other.

5. The device of claim 1, wherein the excitation is provided by a harmonic or random excitation source chosen from a seismic or a noise excitation source.

6. An energy harvesting device comprising: an elongated ferromagnetic cantilevered beam having a base and an opposing end; a transducer chosen from a plurality of piezoceramic elements, a plurality of magnetostrictive materials, or a plurality of capacitor fingers operably connected to the base of the beam, or a coil operably connected at the opposing end of the beam; a first support member for supporting the beam at its base; and two permanent magnets disposed on a second support member; wherein the base end of the beam is operably connected to the support member such that the beam is suspended lengthwise from the support member at its base and the opposing end of the beam is free and is disposed a selected distance above and between the magnets; wherein the beam and transducer are operably configured such that, during operation, the beam is capable of scavenging vibrational energy from an external excitation source and the transducer is capable of converting the vibrational energy into electrical energy; and wherein the device is capable of exhibiting a large-amplitude voltage response when subjected to excitation at about resonance frequency and at any off-resonance frequency.

7. The device of claim 6 further comprising a weighted cantilevered beam for increasing dynamic flexibility.

8. The device of claim 6, wherein the magnets are symmetrically disposed with respect to the beam.

9. The device of claim 6, wherein the piezoceramic elements are disposed on opposing sides of the beam and are connected in parallel to each other.

10. The device of claim 6, wherein the excitation is provided by a harmonic or random excitation source chosen from a seismic or a noise excitation source.

11. An system for powering a load comprising: an electromagnetic, magnetostrictive, electrostatic, or piezo-magneto-elastic power source capable of exhibiting a large-amplitude voltage response when subjected to excitation from an ambient vibration source at about resonance frequency and at any off-resonance frequency; and an electrical load operably electrically connected with the power source.

12. The system of claim 11, wherein the electrical load is an electronics device needing less power to operate than is provided by power output of the power source.

13. The system of claim 11, wherein the electrical load is a rechargeable battery, a capacitor, or a trickle charger.

14. The system of claim 11, wherein the power source is configured comprising: an elongated ferromagnetic cantilevered beam having a base and an opposing end; a transducer chosen from a plurality of piezoceramic elements, a plurality of magnetostrictive materials, or a plurality of capacitor fingers operably connected to the base of the beam, or a coil operably connected at the opposing end of the beam; a first support member for supporting the beam at its base; and two permanent magnets disposed on a second support member; wherein the base end of the beam is operably connected to the support member such that the beam is suspended lengthwise from the support member at its base and the opposing end of the beam is free and is disposed a selected distance above and between the magnets; and wherein the beam and transducer are operably configured such that, during operation, the beam is capable of scavenging vibrational energy from an external excitation source and the transducer is capable of converting the vibrational energy into electrical energy.

15. The system of claim 11, wherein the piezo-magneto-elastic power source is configured comprising: a PZT bender comprising a cantilevered beam with piezoceramic elements; and a plurality of magnets; wherein the beam is disposed a selected distance above and between the magnets, such that the beam is capable of exhibiting a three-equilibrium condition described by electromechanical equations (2) and (3):

x + 2ζx--x(l-x² )-χv = fcosΩt (2)

v + λv + κx = 0 (3) where v is the dimensionless voltage across the load resistance, χ is the dimensionless piezoelectric coupling term in the mechanical equation, K is the dimensionless piezoelectric coupling term in the electrical circuit equation and λ is the reciprocal of the dimensionless time constant (/I x I / R₁C _p where R₁ is the load resistance and C_p is the equivalent capacitance of the piezoceramic layers).

16. The device of claim 15, wherein the excitation is provided by a harmonic or random excitation source chosen from a seismic or a noise excitation source.

17. A sensor system comprising: an electromagnetic, magnetostrictive, electrostatic, or piezo-magneto-elastic power source capable of exhibiting a large-amplitude voltage response when subjected to excitation from an ambient vibration source at about resonance frequency and at any off-resonance frequency; one or more sensors for collecting data, wherein the sensors are operably connected with and electrically powered at least in part by the power source; and a computer-readable storage medium for storing the data.

18. The system of claim 17, wherein the excitation is provided by a harmonic or random excitation source chosen from a seismic or a noise excitation source.

19. A method of monitoring integrity of a structure comprising: providing electrical power output from an electromagnetic, magnetostrictive, electrostatic, or piezo-magneto-elastic power source capable of exhibiting a large-amplitude voltage response when subjected to excitation from an ambient vibration source at about resonance frequency and at any off-resonance frequency; electrically powering one or more sensors with the electrical power output to collect data; and storing the data on a computer-readable storage medium.

20. The device of claim 19, wherein the excitation is provided by a harmonic or random excitation source chosen from a seismic or a noise excitation source.

21. The method of claim 19, wherein the structure being monitored is infrastructure, a vehicle, or a machine.

22. A method of converting mechanical energy to electrical energy comprising: operably connecting a PZT bender to an external source of ambient vibrational energy; transferring the vibrational energy from the source to the PZT bender; converting the energy to electrical energy with piezoceramic elements of the PZT bender; and obtaining a large-amplitude voltage response, when subjected to excitation at about resonance frequency and at any off-resonance frequency.

23. The method of claim 22, wherein the PZT bender is configured to comprise: a cantilevered beam with piezoceramic elements; and a plurality of magnets; wherein the beam is disposed a selected distance above and between the magnets, such that the beam is capable of exhibiting a three-equilibrium condition described by electromechanical equations (2) and (3):

x + 2ζx--x(\ -x² )-χv = fcosΩt (T)

v + λv + κx = 0 (3) where v is the dimensionless voltage across the load resistance, χ is the dimensionless piezoelectric coupling term in the mechanical equation, K is the dimensionless piezoelectric coupling term in the electrical circuit equation and λ is the reciprocal of the dimensionless time constant (λ <x Il R₁C _p where R₁ is the load resistance and C_p is the equivalent capacitance of the piezoceramic layers).

24. The device of claim 22, wherein the excitation is provided by a harmonic or random excitation source chosen from a seismic or a noise excitation source.

25. The method of claim 22, wherein the PZT bender comprises a piezo-magneto- elastic power source configured to comprise: an elongated ferromagnetic cantilevered beam having a base and an opposing end; a plurality of piezoceramic elements operably connected to the base of the beam; a first support member for supporting the beam at its base; and two permanent magnets disposed on a second support member; wherein the base end of the beam is operably connected to the support member such that the beam is suspended lengthwise from the support member at its base and the opposing end of the beam is free and is disposed a selected distance above and between the magnets; and wherein the piezoceramic elements are operably connected in parallel to each other, such that during operation the beam is capable of scavenging vibrational energy from an external excitation source and the piezoceramic elements are capable of converting the vibrational energy into electrical energy.