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CN108225544A - A kind of bilayer composite triangle collapse beam mass block resonator system and its trace detection method - Google Patents

A kind of bilayer composite triangle collapse beam mass block resonator system and its trace detection method Download PDF

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Publication number
CN108225544A
CN108225544A CN201711204428.8A CN201711204428A CN108225544A CN 108225544 A CN108225544 A CN 108225544A CN 201711204428 A CN201711204428 A CN 201711204428A CN 108225544 A CN108225544 A CN 108225544A
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mass block
test system
resonance test
triangle collapse
triangle
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CN108225544B (en
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于虹
张浩东
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Southeast University
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Southeast University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01HMEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H11/00Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by detecting changes in electric or magnetic properties
    • G01H11/06Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by detecting changes in electric or magnetic properties by electric means

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Abstract

The invention discloses a kind of double-deck composite triangle collapse beam mass block resonator system and detection method, system includes substrate and is symmetrically placed in identical the first and second resonance test system of the upper and lower surface texture of substrate;First and second resonance test system includes the pedestal being located on substrate, the top crown being supported on pedestal and the bottom crown positioned at substrate surface center;Top crown includes triangle shape quality block and at least two spanker booms connected to it;Section shin is added between triangle shape quality block and spanker boom tie point, the other end of spanker boom spreads horizontal and vertical type pressure drag resistance, and connect with pedestal respectively;There are the air gaps between bottom crown and triangle collapse beam mass block;Driving voltage one end is connect with the bottom crown of the first and second resonance test system, and the other end is connect respectively with the first and second triangle collapse beam mass blocks.The present invention detects two output signals using external circuits, excludes the influence of temperature, humidity variation to frequency detecting, improves measurement accuracy.

Description

A kind of bilayer composite triangle collapse beam mass block resonator system and its trace detection Method
Technical field
The present invention relates to the MEMS folded beam mass block structures in MEMS, manufactured by silicon micromachining technique System tests the resonant frequency technology of nanoscaled silicon beam, humorous more particularly to a kind of double-deck composite triangle collapse beam mass block Vibrating system and its trace detection method.
Background technology
Microelectromechanical systems (MEMS) refers to using micromachining technology, on a silicon substrate can with batch making, Size is in the micro mechanism microdevice that for example driver, sensor and actuator etc. are integrated in one or system of 1 μm~1mm. System have the characteristics that it is small, at low cost, be easily integrated and produce in batches.
With the continuous development and cooperation of micro mechanical system technology, silicon micro mechanical sensor comes into being, and in silicon microcomputer In the various working methods of tool sensor.Wherein, it is most promising, most attraction be resonance working method.Micro-system is humorous The device that shakes is exactly the working method using this resonance, and then detects resonant frequency.Using it is this detection resonant frequency mode, when Quality m0When changing, and it is capable of detecting when f0Variation.
In recent years, with the progress of microelectric technique processing technology and nanofabrication technique, people have been able to be easy to Produce the clamped beam, cantilever beam and nano wire of nanometer scale.Nanoscaled silicon beam is the typical structure in MEMS, its matter Measure small, power is very low, and the resonant frequency highest for the resonator made is up to GHz, and quality factor are also up to 103, there is 10- The superelevation Mechanical Sensitivity of 24 newton.These excellent performances make nano beam in the generation of high-frequency oscillation signal and processing, superelevation Insensitive mass detection, extra small power, extra small displacement detection, biochemistry sensing etc. have good application prospect.Due to quality It is minimum, the micro variation of the mass block sole mass or extraneous operating condition and environment of nano beam is connected, the resonance of beam can be caused The larger variation of frequency, this is very beneficial for the detection of small-signal, and siliceous gauge block resonator is made to become the main of trace detection Tool.Therefore, mass block resonator is expected to be used for the trace detection of Heavy Metals in Water Environment mercury ion, realizes highly sensitive detection With monitoring.
Resonator structure is divided into three classes:When cantilever beam mass block structure, using static excitation piezoresistive detection.Second is that folding Stoplog mass block structure equally uses electrostatic drive piezoresistive detection.Third, two fixed ends girder construction, using static excitation MOSFET Detection.Cantilever beam mass block structure after mass block has adsorbed ion, is being carried out since mass block is generally in the end of cantilever beam During trace detection, beam extremely easily collapses, and causes to test thrashing;And two fixed ends girder construction is small due to the adsorption area of beam And it is unfavorable for carrying out trace detection.A kind of simple and practicable resonance structure is designed, is frequency test and trace detection method Offer more selects, meaningful.
Existing trace detection mode (1) instrumental method, is widely adopted at present.Shortcoming is then before being carried out to sample Processing, and due to using relatively large spectral instrument, expensive instrument and equipment, cumbersome preparation of samples program are needed, no Can meet the needs of field quick detection.In the pretreatment stage of sample, mercury atom steam will be usually formed, this is easily caused The volatilization and leakage of pernicious gas, it is necessary to stringent safety protection facility and measure are taken, this undoubtedly makes test formality more cumbersome, Also increase the cost of test.(2) electrochemical methods, one be built upon on the basis of the electrochemical properties of substance in the solution Class method, the detection limit of this method is mostly low with accuracy in the method sensitivity of μ g/L magnitudes (3) biological detection, some are also Qualitative detection can only be carried out, the repeatability and stability of testing result are all not good enough, and the sensitivity of detection is also than relatively low.
Invention content
Goal of the invention:To solve the deficiencies in the prior art, it provides a kind of for receiving the double-deck composite of electromechanical trace detection The resonator system of triangle collapse beam mass block structure.
Technical solution:A kind of bilayer composite triangle collapse beam mass block resonator system, including substrate, is symmetrically placed in lining First resonance test system and the second resonance test system on the upper and lower surface in bottom, driving voltage and external circuits;
The first resonance test system is identical with the second resonance test system structure, includes the base positioned at substrate Seat or the top crown that is supported on pedestal and positioned at substrate surface center bottom crown or;Pedestal is set on the week of substrate surface Enclose, top crown include triangle shape quality block or at least two spanker booms connected to it or;Triangle shape quality block is by surrounding Spanker boom supports, and is horizontally disposed with, and section shin is added between spanker boom tie point;The other end of spanker boom spreads horizontal and vertical type respectively It pressure drag resistance or, and is connect with pedestal;Substrate, pedestal, triangle shape quality block and spanker boom form a space, bottom crown and position There are the air gaps between triangle collapse beam mass block among resonance test system;
Driving voltage one end and the first resonance test system and the bottom crown of the second resonance test system connect, the other end and First triangle collapse beam mass block of the first resonance test system and the second triangle collapse beam of the second resonance test system Mass block connects, and forms two output loops;
External circuits with and its connect first resonance test system and the second resonance test system pressure drag resistance formed Favour stone full-bridge.
Preferably, the bottom crown is Al electrodes.
Preferably, the spanker boom of the first resonance test system and the second resonance test system has three, the triangle Form quality gauge block is supported by surrounding three spanker booms, is horizontally disposed with.
Preferably, p-type pressure drag resistance, pedestal and spanker boom material are formed by spreading boron ion in spanker boom and pedestal connecting pin It is N-shaped, has formed insulation knot.
In another embodiment, a kind of trace based on the double-deck composite triangle collapse beam mass block resonator system The triangle collapse beam mass block of detection method, the first resonance test system and the second resonance test system is using identical Compound material makes the first resonance test system and the second resonance test system have identical intrinsic frequency.When the first resonance is surveyed To adsorb specific ion, the second opposite resonance test system or the first resonance are tested for test system or the second resonance test system System does not adsorb specific ion;The quality of first triangle collapse beam mass block or the second triangle collapse beam mass block becomes Change, the quality of the second opposite triangle collapse beam mass block or the first triangle collapse beam mass block does not change;Then, Two resonance test systems give identical driving voltage, and only there are one circuits due to triangle collapse beam matter for two output loops The variation of gauge block quality changes, and another circuit triangle collapse beam mass block does not change;First resonance tests system It is vibrated under electrostatic force with triangle collapse beam mass block with the spanker boom of the second resonance test system, spring beam is by hair Raw bending, then elastic force maximum on outer surface is appeared in just on spanker boom supporting point so that the piezoresistive regions resistance of spanker boom end Rate generating period changes, and opposite two output signals of generation by external circuits, are examined using the method for Wheatstone bridge The cyclically-varying curve of two output signals is surveyed, the frequency of the first and second resonance test system is measured, further measures the One resonance tests the quality of the triangle collapse beam mass block variation of system or the second resonance test system, that is, adsorbs specific ion Quality.
Further, when there is Tiny Mass to reach on triangle collapse beam mass block, the quality of mass block changes, So as to generate the offset of frequency of oscillation, calculation formula is:
f0For the intrinsic frequency of spanker boom, changing values of the △ f for spanker boom frequency, m0For the initial of triangle collapse beam mass block Quality, △ m are the changing value of triangle collapse beam mass block quality after specific ion is adsorbed, and k is constant;
It can be obtained by formula (1) and (2):
Abbreviation obtains:
m0f0 2=m0f0 2+m0△f2+2m0f0△f+△mf0 2+△m△f2+2△m△f×f0(4);
Due to the numerical value very little of △ m and △ f, its quadratic term of dividing out obtains:
△m△f2+2△m△f×f0=0 (5);
Further acquire:
Mass block m can be derived from by formula (5)0Mass change feelings, and then detect water in specific ion concentration.
Advantageous effect:Compared with prior art, the present invention high-frequency vibration test detection during compared to traditional Rectangle folded beam mass block structure is more precise and stable, has the piezoelectric effect of more excellent benefit during high-frequency vibration.And two Only there are one circuit since the variation of mass block quality changes, another loop mass block does not change output loop, profit Output signal is detected with the method for Wheatstone bridge, the influence of temperature, humidity variation to frequency detecting is excluded, improves and measure essence Degree.And as the quality m of mass block0When changing, triangle collapse beam mass block structure resonator system can be more accurate Detect intrinsic frequency f0Variation, i.e. Δ f value, and then preferably characterize m0Variable quantity, meet low cost, at high speed The testable demand in scene.This is simple for structure so that while mass block adsorption area is increased, does not easily cause beam It collapses, can be widely applied to carry out in trace detection using nano beam high frequency vibration characteristic, make that detection is more convenient, numerical value It is more accurate.In addition, the relatively traditional quadrangle of the present invention folds the quality factor q value bigger of girder construction, and as vacuum degree is (humorous The vacuum degree in space where vibrating system) rise, Q values improve more obvious.
Description of the drawings
Fig. 1 is the side structure schematic diagram of the present invention;
Fig. 2 a and Fig. 2 b are two kinds of girder construction top schematic diagrams of different shapes in the present invention;
Fig. 3 is wheatstone bridge circuits figure;
Fig. 4 is the quality factor curve graph of two kinds of triangle collapse beam mass block structures and quadrilateral structure;
Fig. 5 is that the output signal that individual layer mass block structure and dual layer quality block structure generate compares figure.
Specific embodiment
Technical scheme of the present invention is described in detail with reference to the accompanying drawings and examples.
As depicted in figs. 1 and 2, it is of the invention for receiving the double-deck composite triangle collapse beam quality of electromechanical trace detection The resonator system of block structure including substrate 1, is symmetrically placed in the first resonance test system and the second resonance on the upper and lower surface of substrate Test system, driving voltage 4 and external circuits 5.
Wherein, the first resonance test system includes three the first pedestals 21 positioned at substrate, is supported on pedestal First top crown and the first bottom crown positioned at substrate top surface center;First pedestal is set on around substrate top surface, the One triangle collapse beam mass block 22 and three first spanker booms 23 connected to it are used as pole on first as elastic element Plate;Al electrodes 24 positioned at substrate top surface center are used as the first bottom crown.First triangle collapse beam mass block is by around it Three first spanker booms support, be horizontally disposed with, the one end of three of them angle respectively with three first spanker booms is connect, and the first triangle Section shin is added between folded beam mass block and the first spanker boom;The other end of first spanker boom is connect with the first pedestal, and at first strand The other end of beam spreads horizontal and vertical type pressure drag resistance 25 respectively.Substrate, the first pedestal, the first triangle collapse beam mass block And first spanker boom form a space, Al electrodes and the first triangle collapse beam matter among the first resonance test system There are the air gaps between gauge block.
Second resonance test system includes three the second pedestals 31 being located on substrate lower surface, be supported on pedestal the Two top crowns and the second bottom crown positioned at substrate lower surface center;Second pedestal is set on around substrate lower surface, and second Triangle collapse beam mass block 32 and three second spanker booms 33 connected to it are used as the second top crown as elastic element; The Al electrodes 34 of face center are used as the second bottom crown under substrate.Second triangle collapse beam mass block is by around it Three second spanker booms support, be horizontally disposed with, the one end of three of them angle respectively with three second spanker booms is connect, and the second triangle Section shin is added between folded beam mass block and the second spanker boom;The other end of second spanker boom is connect with the second pedestal, and at second strand The other end of beam spreads horizontal and vertical type pressure drag resistance 35 respectively.Substrate, the second pedestal, the second triangle collapse beam mass block And second spanker boom form a space, Al electrodes and the second triangle collapse beam matter among the second resonance test system There are the air gaps between gauge block.
The Al electrodes that 4 one end of driving voltage tests system and the second resonance test system with the first resonance are connect, the other end With the first triangle collapse beam mass block of the first resonance test system and the second triangle collapse of the second resonance test system Beam mass block connects, and forms two output loops.
External circuits 5 are favour stone half-bridge, and the pressure drag resistance being connect with it forms favour stone full-bridge, such as the institutes of Fig. 1 and 3 Show, an arm resistance R of the Wheatstone bridge in Fig. 3j1For the pressure drag resistance 25 in Fig. 1, another arm resistance Rj2For figure Pressure drag resistance 35 in 1, analytic process is as follows:
(1) when triangle collapse beam mass block resonator is not given to apply driving voltage:Rj1=Rj2=R3=R4=Rj0, Rj0The initial resistance of (j=1,2,3,4) for each bridge arm, therefore Vm=0;
(2) when applying driving voltage to triangle collapse beam mass block resonator:
Wherein, △ Rj1For pressure drag resistance Rj1Changing value, △ Rj2For pressure drag resistance Rj2Changing value, △ Rj1pFor pressure drag electricity Resistance is in Rj1The numerical value changed produced by the after-applied excitation resistance of mass change, △ R occur for the mass block at placej1xWith △ Rj2xIt is outer The changing value of pressure drag resistance, the two are equal caused by boundary changes.
It can acquire:
Wherein, Es is input voltage.
Abbreviation obtains:
The spanker boom of first resonance test system and the second resonance test system is with pedestal connecting pin by spreading boron ion shape Into p-type pressure drag resistance, the material of pedestal and spanker boom is N-shaped, to form PN sections;Triangle collapse beam mass block can be with identical Compound material makes the first resonance test system or the second resonance test system have identical intrinsic frequency.When the first resonance is surveyed Test system (or the second resonance test system) is to adsorb specific ion, the second opposite resonance test system (or the first resonance Test system) do not adsorb specific ion;The quality of first triangle collapse beam mass block (or second triangle shape quality block) occurs Variation, the quality of the second opposite triangle collapse beam mass block (or first triangle collapse beam mass block) do not change; Then, two resonance test systems give identical excitation (driving voltage 4), and only there are one circuits due to three for two output loops The variation of angular folded beam mass block quality changes, and another circuit triangle collapse beam mass block does not change;First Resonance tests system and the spanker boom of the second resonance test system shakes with triangle collapse beam mass block under electrostatic force Dynamic, spring beam will bend, then elastic force maximum on outer surface will be appeared on spanker boom supporting point just so that spanker boom end The piezoresistive regions resistivity generating periods variation at end, opposite two output signals of generation, by external circuits 5, using favour this The method of energization bridge detects the cyclically-varying curve of two output signals (voltage or electric current), measures the first and second resonance The frequency (this frequency is not influenced by environmental changes such as temperature, humidity, air pressures) of test system further measures the survey of the first resonance The quality of the triangle collapse beam mass block variation of test system (or the second resonance test system) adsorbs the matter of specific ion Amount.
Principle is specially:When the triangle for thering is Tiny Mass to reach the first resonance test system (or the second resonance test system) When on shape folded beam mass block, the quality of the triangle collapse beam mass block changes, so as to generate the offset of frequency of oscillation, Another triangle collapse beam mass block quality does not change, and frequency of oscillation is constant.When giving two triangle collapse beam mass blocks During identical driving voltage, two output signals are generated, the Wheatstone bridge formed by external circuits and pressure drag resistance measures First resonance tests the frequency of system and the second resonance test system, so that it may push away to reach the first resonance test system (or second Resonance test system) triangle collapse beam mass block on Tiny Mass.For the humorous of triangle collapse beam mass block structure Shake device, it is assumed that test substance is evenly distributed on the triangle collapse beam of the first resonance test system (or the second resonance test system) The frequency shift (FS) △ of system (or the second resonance tests system) high-frequency vibration is then tested on the surface of mass block by first resonance F, measured minimum mass △ m can be by formula △ m=-2m0× △ f/f are acquired.m0、f0Respectively the first resonance tests system The initial mass and resonant frequency of (or the second resonance test system), are determined by process, known to data.
The method plays a significant role in trace detection, the concentration as detected heavy metal ion in water.And not by The influence of the environmental changes such as temperature, humidity, air pressure.Triangle collapse beam mass block can be used the composite material with adsorptivity and inhale The mercury ion of attached solution, the mass block quality adsorbed change, and driving circuit measures f0The value of+△ f, so as to detect solution The concentration of middle mercury ion.
Circular is as follows:
f0For the intrinsic frequency of folded beam, changing values of the △ f for frequency, m0For the initial mass of mass block, △ m are quality The changing value of block quality after specific examples are adsorbed, k is constant.
It can be obtained by formula (1) and (2):
Abbreviation obtains:
m0f0 2=m0f0 2+m0△f2+2m0f0△f+△mf0 2+△m△f2+2△m△f×f0(8);
Due to the numerical value very little of △ m and △ f, its quadratic term of dividing out obtains:
△m△f2+2△m△f×f0=0 (9)
Further acquire:
That is, mass block m can be derived from by formula (5)0Quality change situation, and then detect water in specific ion concentration.
As shown in figure 4, compared with existing quadrangle folded beam mass block structure, triangle collapse beam is measured by experiment The relatively traditional quadrangle of the quality factor q of mass block folds the value bigger of girder construction, and as vacuum degree rises, Q value raising values It is more obvious, wherein Triangular resonators structure as shown in figures 2 a and 2b no matter under any vacuum degree environment its quality factor Q will be far longer than quadrangle resonator, this is because the volume of mass block is reduced with respect to quadrangle, what when vibration was subject to Air damping is also relatively small, and the energy for leading to vibration period consumption is relatively low.Secondly traditional quadrangle resonator vibration Beam has four, and the walking beam of this resonator only has three, the in-fighting smaller when system vibration, therefore Q value highers.Another is heavy The reason of wanting is the vibration that various modes occur during vibration for quadrangle resonator, i.e., upper and lower vibration not only occurs, It there is also the vibration mode of offset from perpendicular, the vibration mode strong influence of the multimode quality factor of resonator, shadow Ring eigentone.And triangle has natural stability, triangle folded beam mass block structure is in the process of vibration In, the form of single mode is only existed, i.e., only keeps upper and lower vibration mode, greatly improves quality factor, overcome quadrangle The influence that resonator is brought due to multimode vibration, so that the testing result of frequency is more accurate.Additionally by test, triangle The piezoresistive effect of shape resonator walking beam end is more obvious, preferably can measure vibration frequency by peripheral circuit, thus works as When the quality of mass block changes, it is easier to measure Δ f by this resonance structure so that test result is more accurate, conveniently, It can be widely applied to carry out the detection of trace using nano beam high frequency vibration characteristic.
Further, as shown in figure 5, for single layer structure (individual layer triangle collapse beam mass block structure) and double-layer structure The output signal that (double-deck composite triangle collapse beam mass block structure) generates is used by the comparison figure after filter circuit Dual channel oscilloscope show comparison result, above channel sine curve be single layer structure output signal, below channel it is remaining Chord curve is the output signal of double-layer structure, and the peak value of single layer structure output signal is 217mV, and double-layer structure is 318mV.It says The output that the method for the external Wheatstone bridge formula circuit of the bright resonator system by double-deck triangle collapse beam mass block structure obtains Signal is better than the method for the external differential frequency circuit of resonator system of individual layer triangle collapse beam mass block structure.

Claims (6)

1. a kind of bilayer composite triangle collapse beam mass block resonator system, it is characterised in that:Including substrate (1), symmetrically put The first resonance in the upper and lower surface of substrate tests system and the second resonance test system, driving voltage (4) and external circuits (5);
The first resonance test system is identical with the second resonance test system structure, includes the pedestal positioned at substrate (21) or (31), the top crown that is supported on pedestal and positioned at the bottom crown (24) in substrate surface center or (34);Pedestal is set Around substrate surface, top crown includes triangle shape quality block (22) or (32) and at least two spanker booms (23) connected to it Or (33);Triangle shape quality block is supported by surrounding spanker boom, is horizontally disposed with, and section shin is added between spanker boom tie point;Stock The other end of beam spreads horizontal and vertical type pressure drag resistance (25) or (35) respectively, and is connect with pedestal;Substrate, pedestal, triangle Form quality gauge block and spanker boom form a space, bottom crown and the triangle collapse beam mass block among resonance test system Between there are the air gaps;
Driving voltage (4) one end and the first resonance test system and the bottom crown of the second resonance test system connect, the other end and First triangle collapse beam mass block of the first resonance test system and the second triangle collapse beam of the second resonance test system Mass block connects, and forms two output loops;
External circuits (5) with and its connect first resonance test system and the second resonance test system pressure drag resistance formed favour Stone full-bridge.
2. a kind of double-deck composite triangle collapse beam mass block resonator system according to claim 1, it is characterised in that: The bottom crown is Al electrodes.
3. a kind of double-deck composite triangle collapse beam mass block resonator system according to claim 1, it is characterised in that: The spanker boom of the first resonance test system and the second resonance test system has three, and the triangle shape quality block is by around it Three spanker booms support, be horizontally disposed with.
4. a kind of double-deck composite triangle collapse beam mass block resonator system according to claim 1, it is characterised in that: P-type pressure drag resistance is formed by spreading boron ion in spanker boom and pedestal connecting pin, pedestal and spanker boom material are N-shaped, have been formed Insulation knot.
It is 5. a kind of based on Claims 1-4 any one of them bilayer composite triangle collapse beam mass block resonator system Trace detection method, it is characterised in that:The triangle collapse beam of the first resonance test system and the second resonance test system Mass block uses identical compound material, and the first resonance test system and the second resonance test system is made to have identical intrinsic frequency Rate.When the first resonance tests system or the second resonance test system to adsorb specific ion, the second opposite resonance test is System or the first resonance test system do not adsorb specific ion;First triangle collapse beam mass block or the second triangle collapse beam matter The quality of gauge block changes, the quality of the second opposite triangle collapse beam mass block or the first triangle collapse beam mass block It does not change;Then, two resonance test systems give identical driving voltage, two output loops only there are one circuit by It changes in the variation of triangle collapse beam mass block quality, another circuit triangle collapse beam mass block does not change; First resonance tests system and the spanker boom of the second resonance test system is issued with triangle collapse beam mass block in electrostatic force Raw vibration, spring beam will bend, then elastic force maximum on outer surface is appeared in just on spanker boom supporting point so that spanker boom The piezoresistive regions resistivity generating periods variation of end, opposite two output signals of generation, by external circuits, using favour this The method of energization bridge detects the cyclically-varying curve of two output signals, measures the frequency of the first and second resonance test system Rate further measures the matter of the triangle collapse beam mass block variation of the first resonance test system or the second resonance test system Amount adsorbs the quality of specific ion.
6. a kind of trace inspection based on double-deck composite triangle collapse beam mass block resonator system according to claim 5 Survey method, it is characterised in that:When there is Tiny Mass to reach on triangle collapse beam mass block, the quality of mass block changes Become, so as to generate the offset of frequency of oscillation, calculation formula is:
f0For the intrinsic frequency of spanker boom, changing values of the △ f for spanker boom frequency, m0For the initial mass of triangle collapse beam mass block, △ m are the changing value of triangle collapse beam mass block quality after specific ion is adsorbed, and k is constant;
It can be obtained by formula (1) and (2):
Abbreviation obtains:
m0f0 2=m0f0 2+m0△f2+2m0f0△f+△mf0 2+△m△f2+2△m△f×f0(4);
Due to the numerical value very little of △ m and △ f, its quadratic term of dividing out obtains:
△m△f2+2△m△f×f0=0 (5);
Further acquire:
Mass block m can be derived from by formula (5)0Mass change feelings, and then detect water in specific ion concentration.
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CN118011043A (en) * 2024-04-10 2024-05-10 中国工程物理研究院电子工程研究所 Micro accelerometer with integrated stress isolation lower polar plate and processing method thereof

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