CN118088822A - A metamaterial unit cell and a low-frequency vibration reduction and isolation device for marine pipelines - Google Patents

Abstract

The invention discloses a metamaterial unit cell and a marine pipeline low-frequency vibration reduction and isolation device, wherein the metamaterial unit cell comprises a substrate and a stress regulator, an outer cylinder body and an inner cylinder body are coaxially arranged on the substrate, a plurality of semicircular buckling blocks are uniformly arranged on the inner wall of the outer cylinder body and the outer wall of the inner cylinder body along the circumferential direction, and the buckling blocks on the inner cylinder body and the outer cylinder body are mutually abutted; the inner cavity of the inner cylinder body is provided with a mass block, and the gap of the inner cavity is filled with elastic filler; the stress regulator is arranged on the outer side of the outer cylinder body and used for extruding the outer cylinder body and regulating the stress applied to the buckling blocks so as to regulate the band gap of the metamaterial unit cell. The marine pipeline low-frequency vibration reduction and isolation device comprises an outer pipe and an inner pipe, wherein an annular cavity is formed between the inner pipe and the outer pipe, and a plurality of metamaterial unit cells are uniformly arranged in the annular cavity in the circumferential direction; the two ends of the annular cavity are closed by end plates; the inner pipe is used for penetrating the marine pipeline, and the end plate is provided with a hole communicated with the inner pipe. The invention can realize low-frequency vibration reduction of the ship pipeline, in particular to wide-frequency low-frequency vibration reduction.

Description

A metamaterial unit cell and a low-frequency vibration reduction and isolation device for marine pipelines

Technical Field

The invention relates to ship vibration reduction and noise reduction, and in particular to a metamaterial unit cell and a low-frequency vibration reduction and isolation device for ship pipelines.

Background technique

The fluid pressure pulsation and low-frequency noise of the pipe wall structure generated by the transmission of water, gas, oil and other media in the pipeline system are one of the main noise sources of ships. Compared with high-frequency noise, low-frequency noise attenuates weakly when propagating in water and is easily detected by enemy sonar. With the increasing requirements for the underwater stealth performance of ships, how to achieve low-frequency vibration reduction and isolation of marine pipelines is an urgent problem to be solved.

Summary of the invention

Purpose of the invention: The purpose of the present invention is to provide a metamaterial unit cell and a low-frequency vibration reduction and isolation device for marine pipelines that can achieve low-frequency vibration reduction.

Technical solution: The metamaterial unit cell described in the present invention includes a substrate and a stress regulator. An outer cylinder and an inner cylinder are coaxially arranged on the substrate. The inner wall of the outer cylinder and the outer wall of the inner cylinder are evenly arranged with a number of semicircular buckling blocks along the circumferential direction. The buckling blocks on the inner and outer cylinders abut against each other. A mass block is arranged in the inner cavity of the inner cylinder, and an elastic filler is filled in the gap in the inner cavity. The stress regulator is arranged on the outside of the outer cylinder, and is used to squeeze the outer cylinder, adjust the stress applied to the buckling blocks, and then adjust the band gap of the metamaterial unit cell.

Furthermore, the mass block includes a cylindrical mass block located in the center and a plurality of fan-shaped long strip mass blocks evenly arranged around the cylindrical mass block.

Furthermore, the base, the outer cylinder and the inner cylinder are an integrated structure.

Furthermore, the stress regulator includes a plurality of arc plates evenly arranged around the outer cylinder, and a radial driving mechanism is arranged at the bottom of the base corresponding to the position of each arc plate, and the radial driving mechanism is used to drive the corresponding arc plate to move radially along the outer cylinder to squeeze the outer cylinder.

Furthermore, the radial driving mechanism includes a track groove and a screw, and a plurality of sliders are arranged in the track groove, wherein the slider at the leftmost end is fixed, and a sleeve is rotatably arranged on the slider at the rightmost end, and limiting edges are arranged at both ends of the sleeve to axially limit the sleeve; the screw passes through the sleeve and cooperates with the sleeve thread; the other sliders except the slider at the rightmost end are provided with threaded holes that cooperate with the screw; the top of each slider is hinged by a connecting rod and a hinge, and the connecting rod and the hinge are lower than the top surface of the track groove; the arc plate is connected to a slider through a connecting block, and the connecting block is a door-type structure, which is arranged on the connecting rod and the hinge; rotating the screw can drive the connecting block to move, and the top surface of the track groove is fixed to the bottom of the base, and a hole for the connecting block to move is provided on the base.

Furthermore, a square head is provided at the end of the screw rod to facilitate the rotation of the screw rod.

The low-frequency vibration reduction and isolation device for marine pipelines described in the present invention comprises an outer tube and an inner tube, an annular cavity is formed between the inner and outer tubes, and a plurality of metamaterial unit cells are evenly arranged in the annular cavity in an annular direction; both ends of the annular cavity are closed by end plates; the inner tube is used for passing the marine pipeline, and the end plate is provided with a hole connected to the inner tube.

Furthermore, the buckling blocks of each metamaterial unit cell are adjusted to have different stresses, so that each metamaterial unit cell has a different band gap, and the band gap width is wider after the band gaps are superimposed.

Furthermore, the metamaterial unit cells arranged in an annular direction in the annular cavity are multi-layered.

Furthermore, the end plate adopts a flange, and a plurality of the marine pipeline low-frequency vibration reduction and isolation devices can be connected and used by the flange according to the length of the marine pipeline.

Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention realizes low-frequency vibration reduction of ship pipelines based on metamaterial unit cells; different stresses are loaded by stress regulators to make the buckling blocks produce different buckling modes, and buckling can change the stiffness of the unit cell structure, reduce the resonance frequency of the unit cell structure, and move the band gap range to low frequency, achieving the effect of adjustable band gap, and then can efficiently control low-frequency sound radiation, suppress low-frequency elastic waves within the band gap range, and attenuate the low-frequency vibration response and transmission of the structure. The present invention can achieve good broadband low-frequency vibration reduction performance, and can effectively improve the vibration reduction and noise reduction effect of ship pipelines.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the structure of a metamaterial unit cell according to an embodiment of the present invention;

FIG2 is a schematic diagram of a radial driving mechanism disposed at the bottom of a substrate in an embodiment of the present invention;

3 is a schematic structural diagram of a radial drive mechanism in an embodiment of the present invention;

FIG4 is a top view of FIG3;

5 is a schematic structural diagram of a low-frequency vibration reduction and isolation device for marine piping in an embodiment of the present invention;

FIG. 6 is a schematic diagram of the internal structure of the low-frequency vibration reduction and isolation device for marine pipelines in an embodiment of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

The reference numerals in the accompanying drawings 1 to 6 are as follows:

1, base; 2, outer cylinder; 3, inner cylinder; 4, buckling block; 5, mass block; 6, arc plate; 7, radial drive mechanism; 701, track groove; 702, slider; 703, screw; 704, sleeve; 705, square head; 706, connecting rod; 707, hinge point; 708, limit edge; 8, outer tube; 9, inner tube; 10, end plate.

As shown in Figures 1 to 4, the embodiment of the present application provides a metamaterial unit cell, including a substrate 1 and a stress regulator, an outer cylinder 2 and an inner cylinder 3 are coaxially arranged on the substrate 1, and the substrate 1, the outer cylinder 2 and the inner cylinder 3 are an integral structure, and the material is aluminum. The inner wall of the outer cylinder 2 and the outer wall of the inner cylinder 3 are evenly arranged with a number of semicircular buckling blocks 4 along the circumferential direction, the buckling blocks 4 extend along the axial direction of the cylinder, and the buckling blocks 4 on the inner and outer cylinders abut against each other, and the buckling blocks 4 are polymer elastic materials. A mass block 5 is arranged in the inner cavity of the inner cylinder 3, and the mass block 5 includes a cylindrical mass block located in the center and four fan-shaped long strip mass blocks evenly arranged around the cylindrical mass block. The mass block is made of stainless steel or tungsten. The inner cavity gap of the inner cylinder 3 is filled with elastic fillers, such as silicone rubber. The stress regulator is arranged on the outside of the outer cylinder 2, used to squeeze the outer cylinder 2, adjust the stress applied to the buckling block 4, and use the conversion of different buckling modes to achieve the effect of adjusting the band gap.

The stress regulator includes a plurality of arc plates 6 evenly arranged around the outer cylinder 2. A radial driving mechanism 7 is arranged at the bottom of the base 1 corresponding to the position of each arc plate 6. The radial driving mechanism 7 is used to drive the corresponding arc plate 6 to move radially along the outer cylinder 2 to squeeze the outer cylinder 2.

Specifically, the radial drive mechanism 7 includes a track groove 701 and a screw 703. A plurality of sliders 702 are arranged in the track groove 701, wherein the slider 702 at the leftmost end is fixed, and a sleeve 704 is rotatably arranged on the slider 702 at the rightmost end. Limiting edges 708 are arranged at both ends of the sleeve 704 for axially limiting the sleeve 704. The screw 703 passes through the sleeve 704 and is threadedly matched with the sleeve 704. The other sliders 702 except the slider 702 at the rightmost end are rotatably arranged on the sleeve 704. 2 is provided with a threaded hole matched with the screw rod 703; the top of each slider 702 is hinged by a connecting rod 706 and a hinge point 707, and the connecting rod 706 and the hinge point 707 are lower than the top surface of the track groove 701; the arc plate 6 is connected to a slider 702 located in the middle position through a connecting block, and the connecting block is a door-shaped structure, which is arranged on the connecting rod 706 and the hinge point 707, so as not to affect the rotation of the connecting rod 706; a square head 705 is provided at the end of the screw rod 703 to rotate the screw rod 703. When the screw rod 703 is rotated, the screw rod 703 is screwed into the threaded hole of the front slider 702. As the screw rod 703 is screwed in, the sliders 702 hingedly connected by the connecting rod 706 approach each other, and the connecting block is driven accordingly, so that the arc plate 6 can move radially to squeeze the outer cylinder 2. The track groove 701 is fixed at the bottom of the base 1, and the top surface of the track groove 701 is in contact with the bottom surface of the base 1. The base 1 is provided with a hole for the connecting block to move.

As shown in Figures 5 and 6, an embodiment of the present application also provides a low-frequency vibration reduction and isolation device for marine pipelines, including an outer tube 8 and an inner tube 9, an annular cavity is formed between the inner and outer tubes, and a number of the metamaterial cells are evenly arranged in the annular cavity. The metamaterial cells arranged in the annular cavity can be one layer or multiple layers. Both ends of the annular cavity are closed by end plates 10. The inner tube 9 is used to pass the marine pipeline, and the end plate 10 is provided with a hole connected to the inner tube 9 (that is, the low-frequency vibration reduction and isolation device for marine pipelines is put on the marine pipeline). In this embodiment, the end plate 10 adopts a flange, so that a plurality of the low-frequency vibration reduction and isolation devices for marine pipelines can be connected and used using the flange according to the length of the marine pipeline.

When in use, the buckling blocks 4 of each metamaterial unit cell are adjusted to have different stresses, so that each metamaterial unit cell has a different band gap, and after the band gaps are superimposed, the band gap width is wider.

The working principle of the present invention is described below.

When the buckling block is stressed, the stiffness of the oscillator (the oscillator includes a mass block and an elastic filler) is adjusted in the unit cell, thereby reducing the transverse and longitudinal vibration mode frequencies of the oscillator. When the frequency of the incident elastic wave is close to the vibration mode of the oscillator, the incident wave will couple with the periodically distributed oscillators (i.e., multiple metamaterial unit cells are periodically arranged), transferring energy to the oscillators of the unit cell, preventing the elastic wave from propagating forward, thereby generating a low-frequency local resonance band gap.

The formula for calculating the band gap range (i.e. the frequency variation law) is as follows:

The vibration isolation components of three-dimensional metamaterials have periodicity and symmetry, so elastic waves satisfy the Bloch theorem when propagating in the vibration isolation components. According to this theorem, any mode of Bloch waves can be analyzed by wave vector k. The frequency range without any wave vector propagation is called a band gap, which means that no elastic wave can be transmitted within this frequency range, so it can be used for sound absorption or vibration isolation. Therefore, it is only necessary to scan along the boundary points of the Brillouin zone and calculate the eigenvector of each point to calculate the dispersion curve of the structure and obtain the band gap range.

For a linear system with translational periodicity, its eigenfield has the form of a Bloch function, expressed as:

u(r)＝ _uk (r) ^eik.r (1)

k is the Bloch wave vector, and its amplitude function u _k has the same translation periodicity as the lattice, that is:

u _k (r + R _n ) = u _k (r) (2)

Where, u(r) represents the Bloch function; is an imaginary unit; u _k represents the displacement of the unit cell, r represents the position, e represents the Euler constant; R _n is a periodic parameter. From lattice theory, we know that when studying the eigenfield of a linear periodic system, the range of the wave vector k can be limited to the first Brillouin zone.

When an elastic wave propagates in a medium, all particles in the same vibration state form a wavefront. For a one-dimensional elastic medium, when the force p(t) excites one end perpendicularly, the elastic wave will propagate along the medium, and the excitation direction is perpendicular to the wavefront, which is a longitudinal wave. The stress τ of a particle in the medium can be expressed as:

Among them, x represents displacement and t represents time;

The velocity of the particle It can be expressed as:

Then the stress and velocity at the particle have the following relationship:

ρ is the density of the medium, and c is the wave speed. For the same medium, ρc is a constant, called mechanical impedance. Taking a one-dimensional medium as an example, the propagation state of elastic waves can be expressed by the following formula:

u(x,t)＝Acos(ωt-|k|x) (6)

Where A is the amplitude; ω = 2πf is the angular frequency; is the wave number, indicating the propagation direction of the wave; λ is the wavelength. Assuming the medium is a continuous, uniform, isotropic material, under the premise of small deformation, the motion state of the particle can be described by the following three equations:

Exercise program:

Geometric equations:

Physics equation:

σ _ij = λθδ _ij + 2μe _ij (9)

σ _ij is the stress of the particle, ρ is the medium density, _fi is the unit volume force, u is the particle displacement; e _ij represents the strain tensor, θ is the volume strain, and μ is the Lame constant of the medium; is the acceleration of the particle; δ _ij is the displacement influence coefficient.

Generally, the particle displacement is regarded as a known quantity, (8) is substituted into (9), the particle stress is expressed as displacement, and then substituted into (7) to solve the particle displacement. The elastic wave equation can generally be expressed as follows:

In the formula, i, j = 1, 2, 3; x ₁ , x ₂ , x ₃ correspond to x, y, z respectively; u ₁ u ₂ u ₃ correspond to u _x u _y u _z respectively.

For isotropic homogeneous media, the above formula can be simplified to:

For the pipe wall, the elastic wave propagates longitudinally along the pipe wall, and the plane perpendicular to the pipe wall is set as the xoy plane, and the particle only produces displacement in the plane. At this time, the wave equation can be decoupled in the direction within the plane and perpendicular to the plane, and the wave equation is decomposed into the xy mode and the z mode, where the vector equation of the xy mode is:

The unit stiffness matrix is established according to the wave equation, and the eigenvector k is solved according to the force balance equation to obtain the dispersion curve of the structure.

The elastic wave equation is u(r,t)=v(r)e ^-iωt , where ω represents the frequency. Substituting it into the isotropic equation, we get the eigenvalue equation:

represents the gradient operator; v(r) represents the potential field.

The matrix form of the equation can be expressed as:

(K-ω ² M)U＝0 (15)

Among them, K is the overall stiffness matrix, M is the mass matrix, and U is the unknown displacement field vector.

The unit cell boundary displacement can be expressed as follows:

U(r+a)＝ei ^(k·a) U(r)(16)

Where a is the periodicity parameter.

By solving the eigenvector k, we can get the dispersion curve of the structure, that is, the dispersion characteristic diagram, and the range of the band gap. At the same time, according to (15), we can get:

is the natural frequency of the system, which is only related to the system itself. According to formula (17), when the stress increases, the stiffness K decreases (the stiffness is only related to EI by definition, and has nothing to do with the internal force. But in fact, the buckling block is an elastic material, and its elastic modulus is much smaller than that of the mass block. When the stress increases, the stiffness of the buckling block decreases, and the decrease in the stiffness of the buckling block proves the decrease in the stiffness of the overall cell, which has been proved by numerical simulation experiments). The mass M is usually unchanged, and the natural frequency ω of the oscillator decreases. For example, when the stiffness decreases from 5200N/M to 2000N/M, the vibration modal frequency of the oscillator in the horizontal and vertical directions decreases from 234Hz to 128Hz, that is, the starting frequency of the band gap decreases to 128Hz. Moreover, only a small stress is required to achieve effective regulation of the band gap. As the stress increases, the band gap region moves toward low frequency as a whole, but due to the increase in stress, the stiffness of the oscillator decreases, and the ability to couple with the incident wave decreases, so the width of the band gap is significantly narrowed.

The width of the band gap depends largely on the equivalent mass (proton energy) of the scatterer in the resonant cavity. The central cylindrical mass block set in the cell and the fan-shaped long mass blocks surrounding it give the oscillator a larger dynamic mass, absorbing more energy during vibration, thereby maximizing the proton energy.

Therefore, in order to solve the problem of increased stress and narrowed band gap, a stress regulator is set outside the buckling block on the basis of maximizing the proton energy. Different loading methods (applying different pressures, such as 0.8MPa, 1MPa, and 1.2MPa) lead to different buckling modes, so that the metamaterial cells produce different band gaps, superimpose the band gaps, achieve the effect of adjustable band gaps, expand the band gap range, and then efficiently control the low-frequency sound radiation of the structure.

Claims (10)

1. A metamaterial unit cell, characterized in that it comprises a substrate (1) and a stress regulator, wherein an outer cylinder (2) and an inner cylinder (3) are coaxially arranged on the substrate (1), a plurality of semicircular buckling blocks (4) are evenly arranged on the inner wall of the outer cylinder (2) and the outer wall of the inner cylinder (3) along the circumferential direction, and the buckling blocks (4) on the inner and outer cylinders abut against each other; a mass block (5) is arranged in the inner cavity of the inner cylinder (3), and an elastic filler is filled in the inner cavity gap; the stress regulator is arranged on the outer side of the outer cylinder (2) and is used to squeeze the outer cylinder (2) and adjust the stress applied to the buckling blocks (4), thereby adjusting the band gap of the metamaterial unit cell. 2. The metamaterial unit cell according to claim 1 is characterized in that the mass block (5) includes a cylindrical mass block located in the center and a plurality of fan-shaped long strip mass blocks evenly arranged around the cylindrical mass block. 3. The metamaterial unit cell according to claim 1 is characterized in that the base (1), the outer cylinder (2) and the inner cylinder (3) are an integrated structure. 4. The metamaterial unit cell according to claim 1 is characterized in that the stress regulator comprises a plurality of arc-shaped plates (6) uniformly arranged around the outer cylinder (2), and a radial driving mechanism (7) is arranged at the bottom of the base (1) at a position corresponding to each arc-shaped plate (6), and the radial driving mechanism (7) is used to drive the corresponding arc-shaped plate (6) to move radially along the outer cylinder (2) to squeeze the outer cylinder (2). 5. The metamaterial unit cell according to claim 4 is characterized in that the radial drive mechanism (7) comprises a track groove (701) and a screw (703), wherein a plurality of sliders (702) are arranged in the track groove (701), wherein the slider (702) at the far left is fixed, and a sleeve (704) is rotatably arranged on the slider (702) at the far right, and limiting edges (708) are arranged at both ends of the sleeve (704) to limit the axial position of the sleeve (704); the screw (703) passes through the sleeve (704) and is threadedly matched with the sleeve (704); and the other sliders (702) except the slider (702) at the far right are rotatably arranged on the slider (702) at the far right. The other slider (702) is provided with a threaded hole matched with the screw rod (703); the top of each slider (702) is hinged through a connecting rod (706) and a hinge point (707), and the connecting rod (706) and the hinge point are lower than the top surface of the track groove (701); the arc plate (6) is connected to a slider (702) through a connecting block, and the connecting block is a door-shaped structure and is arranged on the connecting rod (706) and the hinge point (707); rotating the screw rod (703) can drive the connecting block (707) to move, and the track groove (701) is fixed to the bottom of the base (1), and the base (1) is provided with a hole for the connecting block (707) to move. 6. The metamaterial unit cell according to claim 5, characterized in that a square head (705) is provided at the end of the screw rod (703) to facilitate the rotation of the screw rod (703). 7. A low-frequency vibration reduction and isolation device for marine pipelines, characterized in that it comprises an outer tube (8) and an inner tube (9), an annular cavity is formed between the inner and outer tubes, and a number of metamaterial cells described in any one of claims 1 to 6 are evenly arranged in the annular cavity; both ends of the annular cavity are closed by end plates (10); the inner tube (9) is used to pass the marine pipeline, and the end plate (10) is provided with a hole connected to the inner tube (9). 8. The low-frequency vibration reduction and isolation device for marine pipelines according to claim 7 is characterized in that the buckling blocks (4) of each metamaterial unit cell are adjusted to have different stresses, so that each metamaterial unit cell has a different band gap, and the band gaps have a wider band gap width after superposition. 9. The low-frequency vibration reduction and isolation device for marine pipelines according to claim 7, characterized in that the metamaterial unit cells arranged in annular direction in the annular cavity are multi-layered. 10. The low-frequency vibration reduction and isolation device for marine pipelines according to claim 7 is characterized in that the end plate (10) adopts a flange, and a plurality of the low-frequency vibration reduction and isolation devices for marine pipelines can be connected and used by the flange according to the length of the marine pipeline.