Metamaterial unit cell and low-frequency vibration isolation device for marine pipeline

Abstract

The application discloses a kind of metamaterial unit cell and marine pipeline low-frequency vibration reduction and isolation device, the metamaterial unit cell includes base and stress regulator, coaxially arranged outer cylinder and inner cylinder are provided on base, the inner wall of outer cylinder and the outer wall of inner cylinder are evenly provided with several semicircular buckling blocks along the ring direction, and the buckling blocks on inner cylinder and outer cylinder abut each other;Mass block is arranged in the inner cavity of inner cylinder, and the inner cavity gap is filled with elastic filler;Stress regulator is arranged outside outer cylinder, for extruding outer cylinder, adjusting the stress applied to buckling block, and then adjusting the band gap of metamaterial unit cell.The marine pipeline low-frequency vibration reduction and isolation device includes outer pipe and inner pipe, and annular cavity is formed between inner pipe and outer pipe, a plurality of the metamaterial unit cells are evenly arranged in the annular cavity in the ring direction;Annular cavity is closed by end plate at both ends;Inner pipe is used for penetrating marine pipeline, and the end plate is provided with a hole communicating with the inner pipe.The application can realize low-frequency vibration reduction of marine pipeline, especially wideband low-frequency vibration reduction.

Description

Technical Field

[0001] This invention relates to ship vibration reduction and noise reduction, specifically to a metamaterial unit cell and a low-frequency vibration reduction and isolation device for marine pipelines. Background Technology

[0002] Fluid pressure pulsations and low-frequency noise from pipe wall structures generated during the transmission of media such as water, gas, and oil in pipeline systems are among the main noise sources for ships. Compared to high-frequency noise, low-frequency noise attenuates less when propagating in water, making it easily detectable by enemy sonar. With increasingly stringent requirements for underwater acoustic stealth performance, achieving low-frequency vibration reduction and isolation in marine pipelines is an urgent problem to be solved. Summary of the Invention

[0003] Purpose of the invention: The purpose of this 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.

[0004] Technical solution: The metamaterial unit cell of the present invention includes a substrate and a stress regulator. An outer cylinder and an inner cylinder are coaxially arranged on the substrate. A plurality of semi-circular buckling blocks are uniformly arranged along the circumferential direction on the inner wall of the outer cylinder and the outer wall of the inner cylinder. 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 the gap in the inner cavity is filled with an elastic filler. The stress regulator is arranged on the outside of the outer cylinder and is used to compress the outer cylinder, adjust the stress applied to the buckling blocks, and thus adjust the band gap of the metamaterial unit cell.

[0005] Furthermore, the mass block includes a cylindrical mass block located at the center and several fan-shaped elongated mass blocks uniformly arranged around the cylindrical mass block.

[0006] Furthermore, the base, outer cylinder, and inner cylinder are integrated into a single structure.

[0007] Furthermore, the stress adjuster includes several arc-shaped plates uniformly arranged around the outer cylinder. A radial drive mechanism is provided at the bottom of the base corresponding to the position of each arc-shaped plate. The radial drive mechanism is used to drive the corresponding arc-shaped plate to move radially along the outer cylinder and compress the outer cylinder.

[0008] Furthermore, the radial drive mechanism includes a track groove and a screw. Several sliders are arranged in the track groove, with the leftmost slider fixed and the rightmost slider having a sleeve rotatably mounted on it. Limiting edges are provided at both ends of the sleeve to axially limit its movement. The screw passes through the sleeve and is threadedly engaged with it. The other sliders, except for the rightmost slider, have threaded holes that mate with the screw. The tops of each slider are hinged by a connecting rod and a hinge point, with the connecting rod and hinge point being lower than the top surface of the track groove. An arc-shaped plate is connected to a slider by a connecting block, which is a portal-shaped structure straddling the connecting rod and hinge point. Rotating the screw can drive the connecting block to move. The top surface of the track groove is fixed to the bottom of the base, and holes for the connecting block to move are provided on the base.

[0009] Furthermore, a square head is provided at the end of the screw to facilitate rotation of the screw.

[0010] The marine pipeline low-frequency vibration reduction and isolation device of the present invention includes an outer tube and an inner tube, with an annular cavity formed between the inner and outer tubes. A plurality of metamaterial unit cells are uniformly arranged in the annular cavity in a circumferential direction. The two ends of the annular cavity are closed by end plates. The inner tube is used to run marine pipelines, and the end plate is provided with holes that connect to the inner tube.

[0011] Furthermore, by adjusting the buckling blocks of each metamaterial unit cell to have different stresses, each metamaterial unit cell has a different band gap, and the superposition of band gaps results in a wider band gap width.

[0012] Furthermore, the metamaterial unit cells arranged circumferentially in the annular cavity are multi-layered.

[0013] Furthermore, the end plate adopts a flange, which can be used to connect multiple marine pipeline low-frequency vibration reduction and isolation devices according to the length of the marine pipeline.

[0014] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: This invention achieves low-frequency vibration reduction in ship piping based on metamaterial unit cells; by applying different stresses through a stress regulator, different buckling modes are generated in the buckling blocks. Buckling can change the stiffness of the unit cell structure, reduce the resonant frequency of the unit cell structure, and shift the bandgap range to lower frequencies, achieving an adjustable bandgap effect. This allows for efficient control of low-frequency sound radiation, suppression of low-frequency elastic waves within the bandgap range, and attenuation of the structure's low-frequency vibration response and transmission. This invention achieves excellent broadband low-frequency vibration reduction performance and can effectively improve the vibration reduction and noise reduction effect of ship piping. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the metamaterial unit cell in an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of a radial drive mechanism disposed at the bottom of the base in an embodiment of the present invention;

[0017] Figure 3 This is a schematic diagram of the radial drive mechanism in an embodiment of the present invention;

[0018] Figure 4 yes Figure 3 Top view;

[0019] Figure 5 This is a schematic diagram of the structure of the marine pipeline low-frequency vibration reduction and isolation device in an embodiment of the present invention;

[0020] Figure 6 This 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 Implementation

[0021] The invention will now be further described with reference to the accompanying drawings.

[0022] Appendix Figures 1 to 6 The accompanying figure labels are as follows:

[0023] 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. Limiting edge; 8. Outer tube; 9. Inner tube; 10. End plate.

[0024] like Figures 1 to 4 This application provides a metamaterial unit cell, including a substrate 1 and a stress adjuster. An outer cylinder 2 and an inner cylinder 3 are coaxially arranged on the substrate 1. The substrate 1, outer cylinder 2, and inner cylinder 3 are an integral structure made of aluminum. A plurality of semi-circular buckling blocks 4 are uniformly arranged circumferentially on the inner wall of the outer cylinder 2 and the outer wall of the inner cylinder 3. The buckling blocks 4 extend axially along the cylinder, and the buckling blocks 4 on the inner and outer cylinders abut against each other. The buckling blocks 4 are made of a polymer elastic material. A mass block 5 is disposed within the inner cavity of the inner cylinder 3. The mass block 5 includes a central cylindrical mass block and four fan-shaped elongated mass blocks uniformly arranged around the cylindrical mass block. The mass block is made of stainless steel or tungsten. The voids within the inner cavity of the inner cylinder 3 are filled with an elastic filler, such as silicone rubber. The stress adjuster is located on the outside of the outer cylinder 2 and is used to compress the outer cylinder 2, adjusting the stress applied to the buckling blocks 4. The band gap is adjusted by utilizing the transformation of different buckling modes.

[0025] The stress adjuster includes several arc-shaped plates 6 uniformly arranged around the outer cylinder 2. A radial drive mechanism 7 is provided at the bottom of the base 1 corresponding to the position of each arc-shaped plate 6. The radial drive mechanism 7 is used to drive the corresponding arc-shaped plate 6 to move radially along the outer cylinder 2 and squeeze the outer cylinder 2.

[0026] Specifically, the radial drive mechanism 7 includes a track groove 701 and a screw 703. Several sliders 702 are arranged in the track groove 701, with the leftmost slider 702 fixed and the rightmost slider 702 rotatably mounted on a sleeve 704. Limiting edges 708 are provided at both ends of the sleeve 704 for axial limiting. The screw 703 passes through the sleeve 704 and is threaded into it. The other sliders 702 (excluding the rightmost slider 702) are... 2. A threaded hole is provided to mate with the screw 703; the tops of each slider 702 are hinged via a connecting rod 706 and a hinge point 707, which 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 via a connecting block, which is a portal structure spanning the connecting rod 706 and the hinge point 707, thus not affecting the rotation of the connecting rod 706; a square head 705 is provided at the end of the screw 703 to facilitate rotation of the screw 703. When the screw 703 is rotated, it screws into the threaded hole of the front slider 702. As the screw 703 is screwed in, the sliders 702 connected by the connecting rod 706 move closer to each other, and the connecting block is driven accordingly, thereby enabling the arc plate 6 to move radially to compress the outer cylinder 2. The track groove 701 is fixed to the bottom of the base 1, with the top surface of the track groove 701 abutting against the bottom surface of the base 1. Holes for the moving connecting block are provided on the base 1.

[0027] like Figure 5 and Figure 6 This application also provides a low-frequency vibration damping and isolation device for marine pipelines, including an outer pipe 8 and an inner pipe 9, with an annular cavity formed between the inner and outer pipes. A plurality of metamaterial unit cells are uniformly arranged circumferentially within the annular cavity. The circumferentially arranged metamaterial unit cells in the annular cavity can be a single layer or multiple layers. The annular cavity is closed at both ends by end plates 10. The inner pipe 9 is used to pass through marine pipelines, and the end plate 10 has holes communicating with the inner pipe 9 (i.e., enabling the low-frequency vibration damping and isolation device for marine pipelines to be fitted onto the marine pipelines). In this embodiment, the end plate 10 is a flange, allowing multiple low-frequency vibration damping and isolation devices for marine pipelines to be connected and used according to the length of the marine pipeline.

[0028] In use, the buckling blocks 4 of each metamaterial unit cell are adjusted to have different stresses, so that each metamaterial unit cell has different band gaps. After the band gaps are superimposed, there is a wider band gap width.

[0029] The working principle of this invention is described below.

[0030] When stress is applied to the buckling block, it adjusts the stiffness of the oscillator (which includes a mass block and elastic filler) within the unit cell, thereby reducing the oscillator's transverse and longitudinal vibration mode frequencies. When the frequency of the incident elastic wave approaches the oscillator's vibration mode, the incident wave couples with the periodically distributed oscillators (i.e., multiple metamaterial unit cells arranged periodically), transferring energy to the oscillators in the unit cell and preventing the elastic wave from propagating forward, thus generating a low-frequency localized resonant bandgap.

[0031] The derivation of the formula for calculating the bandgap range (i.e., the frequency variation law) is as follows:

[0032] The vibration isolation components of three-dimensional metamaterials possess periodicity and symmetry, so elastic waves propagating within these components satisfy Bloch's theorem. According to this theorem, any mode of Bloch wave can be analyzed using the wave vector k. The frequency range where no wave vector propagates is called the bandgap, meaning that no elastic wave can propagate within this frequency range. Therefore, this bandgap can be applied to sound absorption or vibration isolation. Thus, by simply scanning around the Brillouin zone boundary points and calculating the eigenvector at each point, the dispersion curve of the structure can be calculated, yielding the bandgap range.

[0033] For a linear system with translational periodicity, its eigenfield has the form of a Bloch function, expressed as:

[0034] u(r)=u k (r)e ik.r (1)

[0035] k is the Bloch wave vector, and its amplitude function u k It possesses the same translational periodicity as the crystal lattice, that is:

[0036] u k (r+R n )=u k (r)(2)

[0037] Where u(r) represents the Bloch function; u is the imaginary unit. k R represents the displacement of the unit cell, r represents the position, and e represents the Euler constant; n The wave vector k is a periodic parameter. According to lattice theory, when studying the eigenfield of a linear periodic system, the range of values ​​for the wave vector k can be restricted to the first Brillouin zone.

[0038] When an elastic wave propagates in a medium, all particles with the same vibration state constitute the wavefront. For a one-dimensional elastic medium, when a force p(t) perpendicularly excites one end of the elastic wave, the elastic wave will propagate along the medium, with the excitation direction perpendicular to the wavefront, making it a longitudinal wave.

[0039]

[0040] Where x represents displacement and t represents time;

[0041] velocity of the particle It can be represented as:

[0042]

[0043] The stress and velocity at the particle point have the following relationship:

[0044]

[0045] ρ is the density of the medium, and c is the wave velocity. For the same medium, ρc is a constant, called mechanical impedance. Taking a one-dimensional medium as an example, the propagation state of an elastic wave can be expressed by the following equation:

[0046] u(x,t)=Acos(ωt-|k|x) (6)

[0047] Where A is the amplitude; ω = 2πf is the angular frequency; Let be the wave number, representing the direction of wave propagation; λ be the wavelength. Assuming the medium is a continuous, homogeneous, isotropic material, under the condition of small deformation, the motion of a particle can be described by the following three equations:

[0048] Exercise range:

[0049]

[0050] Geometric equations:

[0051]

[0052] Physical equations:

[0053] σ ij =λθδ ij +2μe ij (9)

[0054] σ ij Let f be the stress at a point mass, ρ be the density of the medium, and f be the stress at a point mass. i For unit volume force, u is the displacement of the mass point; e ij Let θ represent the strain tensor, θ be the volumetric strain, and μ be the Lamé constant of the medium; δ is the acceleration of the particle; ij This is the displacement influence coefficient.

[0055] Generally, the displacement of the particle is considered a known quantity. Substituting (8) into (9), the stress of the particle is expressed in terms of displacement, and then substituting it into (7) to solve for the displacement of the particle. The elastic wave equation can generally be expressed by the following formula:

[0056]

[0057] In the formula, i,j = 1, 2, 3; x1, x2, x3 correspond to x, y, z respectively; u1u2u3 correspond to u x u y u z .

[0058] For isotropic homogeneous media, the above equation can be simplified to:

[0059]

[0060] For the pipe wall, the elastic wave propagates longitudinally along the wall. Let the plane perpendicular to the wall be the xoy plane; the particle only undergoes displacement within this plane. In this case, the wave equation can be decoupled between the in-plane and the direction perpendicular to the plane. The wave equation is decomposed into xy and z modes, where the vector equation for the xy mode is:

[0061]

[0062]

[0063] The element stiffness matrix is ​​established based on the wave equation, and the eigenvector k is solved according to the force balance equation to obtain the dispersion curve of the structure.

[0064] The equation for an elastic wave is u(r,t)=v(r)e -iωt ω represents frequency. Substituting this into the isotropic equation yields the eigenvalue equation:

[0065]

[0066] represents the gradient operator; v(r) represents the potential field.

[0067] The matrix form of the equation can be represented as:

[0068] (K-ω 2 M)U=0 (15)

[0069] Where K is the global stiffness matrix, M is the mass matrix, and U is the unknown displacement field vector.

[0070] The unit cell boundary displacement can be expressed by the following formula:

[0071] U(r+a)=e i(k·a) U(r)(16)

[0072] Where a is a periodic parameter.

[0073] Solving for the eigenvector k yields the dispersion curve of the structure, i.e., the dispersion characteristic diagram, from which the bandgap range can be determined. Simultaneously, based on the variation of (15), we can obtain:

[0074]

[0075] The natural frequency of the system is only related to the system itself. According to formula (17), when the stress increases, the stiffness K decreases. (Stiffness is defined to be only related to EI and has no relation to internal force. However, in reality, 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 overall cell stiffness, as demonstrated by numerical simulation experiments.) The mass M usually remains unchanged, so the natural frequency ω of the oscillator decreases. For example, when the stiffness decreases from 5200 N / M to 2000 N / M, the vibration mode frequencies of the oscillator in the horizontal and vertical directions decrease from 234 Hz ​​to 128 Hz, that is, the starting frequency of the bandgap decreases to 128 Hz. Moreover, only a small amount of stress is needed to achieve effective control of the bandgap. As the stress increases, the bandgap region shifts to lower frequencies 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 bandgap becomes significantly narrower.

[0076] The width of the band gap largely depends on the equivalent mass (proton energy) of the scatterer in the resonant cavity. The central cylindrical mass block and the surrounding fan-shaped elongated mass blocks within the cell give the oscillator a larger dynamic mass, allowing it to absorb more energy during vibration and thus maximize the proton energy.

[0077] Therefore, in order to solve the problem of increased stress and narrowing band gap, based on maximizing proton energy, a stress regulator is set on the outside of the buckling block. Different loading methods (applying different pressures, such as 0.8MPa, 1MPa, and 1.2MPa) lead to different buckling modes, which causes different band gaps to be generated in the metamaterial cells. By superimposing the band gaps, the effect of adjustable band gap is achieved, the band gap range is expanded, and thus the low-frequency acoustic radiation of the structure is effectively controlled.

Claims

1. A metamaterial unit cell, characterized in that, The device includes a base (1) and a stress adjuster. An outer cylinder (2) and an inner cylinder (3) are coaxially arranged on the base (1). Several semi-circular buckling blocks (4) are uniformly arranged along the circumferential direction on the inner wall of the outer cylinder (2) and the outer wall of the inner cylinder (3). 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 the cavity is filled with an elastic filler. The stress adjuster is arranged on the outside of the outer cylinder (2) and is used to squeeze the outer cylinder (2) to adjust the stress applied to the buckling blocks (4), thereby adjusting the band gap of the metamaterial unit cell. The stress adjuster includes several arc-shaped plates (6) uniformly arranged around the outer cylinder (2). A radial drive mechanism (7) is provided at the bottom of the base (1) corresponding to the position of each arc-shaped plate (6). The radial drive mechanism (7) is used to drive the corresponding arc-shaped plate (6) to move radially along the outer cylinder (2) and squeeze the outer cylinder (2). The radial drive mechanism (7) includes a track groove (701) and a screw (703). Several sliders (702) are arranged in the track groove (701). The leftmost slider (702) is fixed, and a sleeve (704) is rotatably arranged on the rightmost slider (702). Limiting edges (708) are provided at both ends of the sleeve (704) to axially limit the sleeve (704). The screw (703) passes through the sleeve (704) and is threadedly engaged with the sleeve (704). The other sliders (702) except the rightmost slider (702) are opened to engage with the screw. The threaded hole of the rod (703) is matched; the top of each slider (702) is hinged by the connecting rod (706) and the 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) by a connecting block, the connecting block is a gate-shaped structure, spanning the connecting rod (706) and the hinge point (707); rotating the screw (703) can drive the connecting block (707) to move, the track groove (701) is fixed to the bottom of the base (1), and the base (1) has a hole for the connecting block (707) to move.

2. The metamaterial unit cell according to claim 1, characterized in that, The mass block (5) includes a cylindrical mass block located at the center and several fan-shaped elongated mass blocks uniformly arranged around the cylindrical mass block.

3. The metamaterial unit cell according to claim 1, characterized in that, The base (1), outer cylinder (2) and inner cylinder (3) are an integral structure.

4. The metamaterial unit cell according to claim 1, characterized in that, A square head (705) is provided at the end of the screw (703) to allow the screw (703) to be rotated.

5. A low-frequency vibration damping and isolation device for marine pipelines, characterized in that, It includes an outer tube (8) and an inner tube (9), with an annular cavity formed between the inner and outer tubes. Several metamaterial unit cells as described in any one of claims 1 to 4 are uniformly arranged in the annular cavity. The two ends of the annular cavity are closed by end plates (10). The inner tube (9) is used to run marine pipelines, and the end plate (10) is provided with holes that connect to the inner tube (9).

6. The marine pipeline low-frequency vibration reduction and isolation device according to claim 5, 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 different band gaps, and the superposition of band gaps results in a wider band gap width.

7. The marine pipeline low-frequency vibration damping and isolation device according to claim 5, characterized in that, The annular cavity contains multiple layers of metamaterial unit cells arranged circumferentially.

8. The marine pipeline low-frequency vibration damping and isolation device according to claim 5, characterized in that, The end plate (10) adopts a flange, and multiple marine pipeline low-frequency vibration reduction and isolation devices can be connected and used according to the length of the marine pipeline.

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