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

Abstract

Multi-material vibration damper bushing for isolating low-frequency vibration in marine pipelines on ships. The damper has semi-circular buckling bumpers 4 between outer cylinder 2 and inner cylinder

Description

[0001] The present disclosure relates to the technical field of vibration and noise reduction of ships, and particularly relates to a metamaterial unit cell and a low-frequency vibration reduction and isolation device for marine pipelines. BACKGROUND

[0002] Fluid pressure pulsation and low-frequency noise in pipe wall structures generated during the transmission of water, gas, oil and other media in pipeline systems are main noise sources of ships. Compared to high-frequency noise, low-frequency noise attenuates weakly when propagating in water and may be easily detected by an enemy sonar. As increasingly rigorous requirements are raised for the acoustic stealth performance of ships, how to solve the problem of low-frequency vibration reduction and isolation of marine pipelines has become a problem to be solved urgently. SUMMARY

[0003] Invention objective: an objective of the present disclosure is to provide a metamaterial unit cell and a low-frequency vibration reduction and isolation device for marine pipelines capable of achieving low-frequency vibration reduction.

[0004] Technical solution: the metamaterial unit cell of the present disclosure includes a substrate and a stress regulator, where the substrate is coaxially provided with an outer cylinder and an inner cylinder, a plurality of semi-circular buckling blocks are evenly arranged on an inner wall of the outer cylinder and an outer wall of the inner cylinder along a circumferential direction, and the buckling blocks on the inner cylinder and the outer cylinder abut against each other; a mass block is arranged inside an inner cavity of the inner cylinder, and voids in the inner cavity of the inner cylinder are filled with an elastic filler; and the stress regulator is arranged on an outer side of the outer cylinder to extrude the outer cylinder and adjust a stress applied to the buckling blocks, so that the bandgaps of the metamaterial unit cells can be adjusted.

[0005] Further, the mass block includes a cylindrical mass block in the middle thereof and a plurality of sector-shaped mass blocks of a long strip shape arranged evenly around the cylindrical mass block.

[0006] Further, the substrate, the outer cylinder and the inner cylinder are of an integrated structure.

[0007] Further, the stress regulator includes a plurality of arc-shaped plates evenly arranged around the outer cylinder, a radial driving mechanism is arranged at the bottom of the substrate corresponding to a position of each of the arc-shaped plates, and the radial driving mechanism is configured to drive a corresponding arc-shaped plate to move radially along the outer cylinder so as to extrude the outer cylinder.

[0008] Further, the radial driving mechanism includes a track groove and a screw rod, a plurality of sliding blocks are arranged in the track groove, the far-left sliding block is fixed and the far-right sliding block is rotatably provided with a sleeve, and a limit edge is arranged at both ends of the sleeve respectively to axially limit the sleeve; the screw rod penetrates through and is in threaded fit with the sleeve; a threaded hole in fit with the screw rod is formed on each of the sliding blocks except for the far-right sliding block; tops of all sliding blocks are hinged through connecting rods and hinge points, and the connecting rods and the hinge points are below a top surface of the track groove; the arc-shaped plates are connected to a sliding block through the connecting blocks, and the connecting blocks of a door-like structure span over the connecting rods and the hinge points; and the screw rod is rotated to drive the connecting blocks to move, the track groove is fixed at the bottom of the substrate, and holes are formed in the substrate for the movement of the connecting blocks.

[0009] Further, a square head is arranged at an end portion of the screw rod to rotate the screw rod.

[0010] The low-frequency vibration reduction and isolation device for marine pipelines of the present disclosure includes an outer pipe and an inner pipe, where an annular cavity is formed between the inner pipe and the outer pipe, and a plurality of the metamaterial unit cells are evenly arranged inside the annular cavity in the circumferential direction; both ends of the annular cavity are sealed with an end plate; and the inner pipe is configured for marine pipelines to penetrate through, and holes in communication with the inner pipe are formed on the end plate.

[0011] Further, the buckling blocks configured for adjusting each metamaterial unit cell have different stresses, so that each metamaterial unit cell has different bandgaps, and after the superposition of bandgaps, a wider bandgap width is achieved.

[0012] Further, a plurality of layers of the metamaterial unit cells can be arranged inside the annular cavity in the circumferential direction.

[0013] Further, the end plate is of a flange structure, so that a plurality of the low-frequency vibration reduction and isolation devices can be connected through flanges according to specific lengths of marine pipelines.

[0014] Beneficial effects: compared to the prior art, the present disclosure has the following significant advantages: the present disclosure achieves low-frequency vibration reduction of marine pipelines through the metamaterial unit cells; by applying different stresses through the stress regulator, different buckling modes of the buckling blocks are generated; through buckling, the present disclosure changes the stiffness of the unit cell structure, reduces the resonance frequency of a unit cell structure, and moves the bandgap range towards a lower frequency, so that an adjustable bandgap effect is achieved, low-frequency acoustic radiation is effectively controlled, low-frequency elastic waves within the bandgap range are suppressed, and the low-frequency vibration response and transmission of the structure attenuate. The present disclosure is capable of achieving good broadband low-frequency vibration reduction performance and effectively improving the effect of vibration and noise reduction of marine pipelines. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] FIG. lisa structural schematic diagram of a metamaterial unit cell in an embodiment of the present disclosure.

[0016] FIG. 2 is a schematic diagram of a radial driving mechanism arranged at the bottom of a substrate in an embodiment of the present disclosure.

[0017] FIG. 3 is a structural schematic diagram of a radial driving mechanism in an embodiment of the present disclosure.

[0018] FIG. 4 is a top view of FIG. 3.

[0019] FIG. 5 is a structural schematic diagram of a low-frequency vibration reduction and isolation device for marine pipelines in an embodiment of the present disclosure.

[0020] FIG. 6 is a schematic diagram of an internal structure of a low-frequency vibration reduction and isolation device for marine pipelines in an embodiment of the present disclosure. DETAILED DESCRIPTIONS OF THE EMBODIMENTS

[0021] The present disclosure will be further described below with reference to the accompanying drawings.

[0022] The reference numerals in FIGs. 1-6 are as follows:

[0023] 1, substrate; 2, outer cylinder; 3, inner cylinder; 4, buckling block; 5, mass block; 6, arc-shaped plate; 7, radial driving mechanism; 701, track groove; 702, sliding block; 703, screw rod; 704, sleeve; 705, square head; 706, connecting rod; 707, hinge point; 708, limit edge; 8, outer pipe; 9, inner pipe; and 10, end plate.

[0024] As shown in FIGs. 1-4, in an embodiment of the present disclosure, there is provided a metamaterial unit cell, and the metamaterial unit cell includes a substrate 1 and a stress regulator, where the substrate 1 is coaxially provided with an outer cylinder 2 and an inner cylinder 3, and the substrate 1, the outer cylinder 2 and the inner cylinder 3 are of an integrated structure and made of aluminum. A plurality of semi-circular buckling blocks 4 are evenly arranged on an inner wall of the outer cylinder 2 and an outer wall of the inner cylinder 3 along a circumferential direction, the buckling blocks 4 extend along an axial direction of the cylinders, and the buckling blocks 4 on the inner cylinder and the outer cylinder abut against each other, and the buckling blocks 4 are made of an elastic polymer material. A mass block 5 is arranged inside an inner cavity of the inner cylinder 3, and the mass block 5 includes a cylindrical mass block in the middle thereof and four sector-shaped mass blocks of a long strip shape arranged evenly around the cylindrical mass block. The mass blocks are made of stainless steel or tungsten. Voids in the inner cavity of the inner cylinder 3 are filled with an elastic filler, such as silicone rubber. The stress regulator is arranged on an outer side of the outer cylinder 2 to extrude the outer cylinder 2 and adjust a stress applied to the buckling blocks 4, and different buckling modes can be switched to achieve the effect of bandgap adjustment.

[0025] The stress regulator includes a plurality of arc-shaped plates 6 evenly arranged around the outer cylinder 2, a radial driving mechanism 7 is arranged at the bottom of the substrate 1 corresponding to a position of each of the arc-shaped plates 6, and the radial driving mechanism 7 is configured to drive a corresponding arc-shaped plate 6 to move radially along the outer cylinder 2 so as to extrude the outer cylinder 2.

[0026] Specifically, the radial driving mechanism 7 includes a track groove 701 and a screw rod 703, a plurality of sliding blocks 702 are arranged in the track groove 701, the far-left sliding block 702 is fixed and the far-right sliding block 702 is rotatably provided with a sleeve 704, and a limit edge 708 is arranged at both ends of the sleeve 704 respectively to axially limit the sleeve 704; the screw rod 703 penetrates through and is in threaded fit with the sleeve 704; a threaded hole in fit with the screw rod 703 is formed on each of the sliding blocks 702 except for the far-right sliding block 702; tops of all sliding blocks 702 are hinged through connecting rods 706 and hinge points 707, and the connecting rods 706 and the hinge points 707 are below a top surface of the track groove 701; the arc-shaped plates 6 are connected to a sliding block 702 at a middle position through the connecting blocks, and the connecting blocks of a door-like structure span over the connecting rods 706 and the hinge points 707, so that rotation of the connecting rods 706 is not affected; and a square head 705 is arranged at an end portion 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 sliding block 702 in front, and as the screw rod 703 is further screwed into, the sliding blocks 702 connected to each other in a hinged manner by means of the connecting rods 706 approach each other, and the connecting blocks are driven, so that the arc-shaped plates 6 move radially to extrude the outer cylinder 2. The track groove 701 is fixed at the bottom of the substrate 1, a top surface of the track groove 701 abuts against a bottom surface of the substrate 1, and holes are formed in the substrate 1 for the movement of the connecting blocks.

[0027] As shown in FIGs. 5 and 6, in an embodiment of the present disclosure, there is further provided a low-frequency vibration reduction and isolation device for marine pipelines, and the device includes an outer pipe 8 and an inner pipe 9. An annular cavity is formed between the inner pipe 9 and the outer pipe 8, and a plurality of the metamaterial unit cells are evenly arranged inside the annular cavity in the circumferential direction. One or more layers of the metamaterial unit cells can be arranged inside the annular cavity in the circumferential direction. Both ends of the annular cavity are sealed with an end plate 10. The inner pipe 9 is configured for marine pipelines to penetrate through, and holes in communication with the inner pipe 9 are formed on the end plate 10 (that is, used to achieve the purpose that the low-frequency vibration reduction and isolation device is sleeved on the maritime pipeline). In this embodiment, the end plate 10 is of a flange structure, so that a plurality of the low-frequency vibration reduction and isolation devices can be connected through flanges according to specific lengths of marine pipelines.

[0028] In use, the buckling blocks 4 configured for adjusting each metamaterial unit cell have different stresses, so that each metamaterial unit cell has different bandgaps, and after the superposition of bandgaps, a wider bandgap width is achieved.

[0029] A working principle of the present disclosure is described below.

[0030] After a stress is applied to a buckling block, stiffness of an oscillator is adjusted in a unit cell (the oscillator includes a mass block and an elastic filler), so that a vibration modal frequency of the oscillator in both the horizontal and vertical directions declines. When the frequency of an incident elastic wave approaches the vibration modal frequency of the oscillator, the incident wave will be coupled with periodically distributed oscillators (that is, a plurality of metamaterial unit cells are arranged periodically), and energy is transferred to the oscillators of unit cells to prevent the elastic wave from propagating forward, so that a low-frequency locally resonance bandgap is generated.

[0031] An equation for calculating a bandgap range (i.e., a low of frequency variation) is derived as follows:

[0032] A vibration isolation component made of a three-dimensional metamaterial has the characteristics of periodicity and symmetry, so the elastic wave propagates in a vibration isolation element in line with a Bloch theorem. According to this theorem, any mode of Bloch wave can be analyzed by using a wave vector k, and a frequency range without any wave vector propagation is called a bandgap, which indicates that within this frequency range, no elastic wave can be propagated, so it can be used for sound absorption or vibration isolation. Therefore, only by scanning around boundary points of a Brillouin zone and calculating values of an eigen wave vector at each point, a dispersion curve of structure can be calculated to obtain a bandgap range.

[0033] For a linear system with translational periodicity, a Bloch function of an eigenfield is expressed as:

[0034] u^ = uk^e (i) u

[0035] where AAs a Bloch wave vector, and an amplitude function * thereof has the same translational periodicity as that of a lattice, that is:

[0036] Uk^r + Rn) = uk(r) (2)

[0037] where represents the Bloch function; z - is an imaginary unit; Uk represents the displacement of a unit cell, r represents a position, and e is an Euler-Mascheroni constant; and "is a periodic parameter. According to a lattice theory, when studying the eigenfield of a linear periodic system, a value range of the wave vector k can be limited to the first Brillouin zone.

[0038] When an elastic wave is propagated in a medium, all particles with a same vibration state constitute a wavefront. When an acting force P^ perpendicularly excites one end of a one-dimensional elastic medium, the elastic wave will be propagated along the medium, with a direction of excitation perpendicular to the wavefront, and a longitudinal wave is formed. A stress T on a particle in the medium can be expressed as: / A f = -^--)

[0039] c (3)

[0040] where, x represents displacement, and t represents time;

[0041] a velocity u of the particle can be expressed as: 1 / u =—p(t—)

[0042] Pc c (4)

[0043] there exists the following relationship between the stress and the velocity at the particle:

[0044] T = ~Pcil (5)

[0045] where P is a density of the medium, and c is a wave speed. For the same medium, Pc is a constant known as mechanical impedance. Taking a one-dimensional medium as an example, a propagation state of an elastic wave can be expressed as follows:

[0046] M(x’0 = ^cos(®t-|k|x) h=—

[0047] where A is an amplitude; a ■’ is an angular frequency; 2 js a wave number, indicating a direction of wave propagation; and is a wavelength. When the medium is assumed as a continuous, uniform, isotropic material, on the premise of small deformation, a motion state of a particle can be described by the following three equations:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] Amotion equation: a^+pf^pu, (7) A geometric equation: 1 z 2 7 7 (8) A physical equation: ^=2^+2 / / ^ (9)

[0054] represents a stress of the particle, P is a density of the medium, is a force per £ unit volume, and 11 represents the displacement of the particle; 5 represents a strain tensor, P is a volumetric strain, and P is a lame constant of the medium; is an accelerated velocity of the particle; and 0 is a displacement influence coefficient.

[0055] Generally, the displacement of the particle is considered to be known. The equation (8) is substituted into the equation (9), the stress of the particle is expressed by the displacement, and then it is substituted into the equation (7) to solve the displacement of the particle. An elastic wave equation can generally be expressed as follows: ' 5 du 5 du du Pii<=

[0056] + + + + + (10)

[0057] where z’^ . M2A correspond to x^y^z respectively; and U\U2U3 u u u correspond to x y z respectively.

[0058] For an isotropic and homogeneous medium, the above equation can be simplified as:

[0059] + + (n)

[0060] When the elastic wave is propagated along a longitudinal direction of a pipe wall, a plane perpendicular to the pipe wall is assumed as an xoy plane, and the displacement of the particle only occurs within the plane. In this case, the elastic wave equation can be decoupled within the plane and in a direction perpendicular to the plane, and is decomposed into vector equations of an xy mode and a z mode, where the vector equations of the xy mode are expressed as: du du du 5 : / \^x '"y, = — 2(r)(—- +—^) +— 2 / / (^)—- du du

[0061] J (12)

[0062]

[0063] d\ dt du du du du du 5 : / J" d ~ . d r ^xx = — 2(r)(—- +—-) +— 2 / / (r)—- +— / / (r)(—- +—-) J (13) Based on the wave equations, an element stiffness matrix is established, and then the eigen wave vector k is solved according to a force balance equation to obtain the dispersion curve of the structure.

[0064] The elastic wave equation is v(f)e , where a represents the frequency, and an eigen equation is obtained as follows after substitution into the isotropic equation:

[0065] -P®2'<'') = U + Z0V(V^^^

[0066] where represents a gradient operator; and represents a potential field.

[0067] A matrix form of the equation can be expressed as:

[0068] (K-cd2M)U = 0 q5)

[0069] where K is an overall stiffness matrix, M is a mass matrix, and U is an unknown displacement field vector.

[0070] The displacement at a boundary of a unit cell can be expressed as:

[0071] U(r+a) = eKka)U(r)

[0072] where a is a periodic parameter.

[0073] The eigen wave vector k is solved to obtain the dispersion curve of the structure, i.e., a frequency dispersion characteristic diagram, and a bandgap range can be obtained. Further, the following equation can be obtained based on the variation of the equation (15): co =\ —

[0074] V M (17)

[0075] A natural frequency of system is only related to the system. According to the equation (17), when the stress increases, the stiffness K decreases (by definition, the stiffness is only related to EI and is not related to an internal force. However, in reality, the buckling blocks are made of an elastic material with a much lower elastic modulus than that of the mass blocks. When the stress increases, the stiffness of the buckling blocks decreases, indicating that the overall stiffness of unit cells decreases, which is proven by numerical simulation experiments). When the mass matrix M usually remains unchanged, the natural frequency ® of the oscillator decreases. For example, when the stiffness decreases from 5200 N / M to 2000 N / M, the vibration modal frequency of the oscillator in the horizontal and vertical directions decrease from 234 Hz to 128 Hz, that is, a starting frequency of the bandgap decreases to 128 Hz. Further, only a relatively small amount of stress is needed to effectively adjust and control the bandgap. As the stress increases, a bandgap region as a whole moves towards a lower frequency, but due to an increase in the stress, the stiffness of the oscillator decreases, and the capacity of coupling with the incident wave decreases, so the width of the bandgap is narrowed greatly.

[0076] The width of the bandgap largely depends on an equivalent mass (proton energy) of scatters in a resonant cavity, and the cylindrical mass block in the middle thereof and the four sector-shaped mass blocks of a long strip shape arranged evenly around the cylindrical mass block within the unit cell enable the oscillator to have a larger dynamic mass and absorb more energy during vibration, thereby maximizing the proton energy.

[0077] Therefore, to solve the problem of bandgap narrowing with the stress increase, on the basis of maximizing the proton energy, the stress regulator is arranged outside the buckling blocks. Different loading methods (applying different pressures, such as 0.8 MPa, 1 MPa, 1.2 MPa) cause different buckling modes, resulting in that there are different bandgaps for the metamaterial unit cells. By superimposing the bandgaps, an adjustable bandgap effect is achieved, and the bandgap range is expanded, thereby efficiently controlling low-frequency acoustic radiation of the structure.

Claims

What it claimed is:

1. A metamaterial unit cell, comprising a substrate and a stress regulator, wherein the substrate is coaxially provided with an outer cylinder and an inner cylinder, a plurality of semi-circular buckling blocks are evenly arranged on an inner wall of the outer cylinder and an outer wall of the inner cylinder along a circumferential direction, and the buckling blocks on the inner cylinder and the outer cylinder abut against each other; a mass block is arranged inside an inner cavity of the inner cylinder, and voids in the inner cavity of the inner cylinder are filled with an elastic filler; and the stress regulator is arranged on an outer side of the outer cylinder to extrude the outer cylinder and adjust a stress applied to the buckling blocks, so that the bandgaps of the metamaterial unit cells can be adjusted.

2. The metamaterial unit cell according to claim 1, wherein a mass block is arranged inside an inner cavity of the inner cylinder and the mass block comprises a cylindrical mass block in the middle thereof and a plurality of sector-shaped mass blocks of a long strip shape arranged evenly around the cylindrical mass block.

3. The metamaterial unit cell according to claim 1, wherein the substrate, the outer cylinder and the inner cylinder are of an integrated structure.

4. The metamaterial unit cell according to claim 1, wherein the stress regulator comprises a plurality of arc-shaped plates evenly arranged around the outer cylinder, a radial driving mechanism is arranged at the bottom of the substrate corresponding to a position of each of the arc-shaped plates, and the radial driving mechanism is configured to drive a corresponding arc-shaped plate to move radially along the outer cylinder so as to extrude the outer cylinder.

5. The metamaterial unit cell according to claim 4, wherein the radial driving mechanism comprises a track groove and a screw rod, a plurality of sliding blocks are arranged in the track groove , the far-left sliding block is fixed and the far-right sliding block is rotatably provided with a sleeve, and a limit edge is arranged at both ends of the sleeve respectively to axially limit the sleeve; the screw rod penetrates through and is in threaded fit with the sleeve; a threaded hole in fit with the screw rod is formed on each of the sliding blocks except for the far-right sliding block; tops of all sliding blocks are hinged through connecting rods and hinge points, and the connecting rods and the hinge points are below a top surface of the track groove; the arc-shaped plates are connected to a sliding block through the connecting blocks, and the connecting blocks of a door-like structure span over the connecting rods and the hinge points; and the screw rod is rotated to drive the connecting blocks to move, the track groove is fixed at the bottom of the substrate, and holes are formed in the substrate for the movement of the connecting blocks.

6. The metamaterial unit cell according to claim 5, wherein a square head is arranged at an end portion of the screw rod to rotate the screw rod.

7. A low-frequency vibration reduction and isolation device for marine pipelines, comprising an outer pipe and an inner pipe, an annular cavity is formed between the inner pipe and the outer pipe, and a plurality of the metamaterial unit cells according to claim 1 are evenly arranged inside the annular cavity in the circumferential direction; and the inner pipe is configured for marine pipelines to penetrate through, and holes in communication with the inner pipe are formed on the end plate.

8. The low-frequency vibration reduction and isolation device for marine pipelines according to claim 7, wherein the buckling blocks configured for adjusting each metamaterial unit cell have different stresses, so that each metamaterial unit cell has different bandgaps, and after the superposition of bandgaps, a wider bandgap width is achieved.

9. The low-frequency vibration reduction and isolation device for marine pipelines according to claim 7, wherein a plurality of layers of the metamaterial unit cells can be arranged inside the annular cavity in the circumferential direction.

10. The low-frequency vibration reduction and isolation device for marine pipelines according to claim 7, wherein the end plate is of a flange structure, so that a plurality of the low-frequency vibration reduction and isolation devices can be connected through flanges according to specific lengths of marine pipelines.

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