Medium and low frequency vibration isolation plate based on photonic crystal structure
By adopting a phonon crystal structure and a trampoline spiral phonon crystal single cell array in the vibration isolation plate, the problem that the band gap frequency is not low enough and the structural mass is heavier when facing vibration and noise problems in different frequency bands is solved, effectively suppressing and isolation of medium and low frequency elastic waves is achieved, and the band gap frequency is reduced, and the relative bandwidth is greater than 50%, while reducing the overall structural weight of the vibration isolation plate.
Patent Information
- Application Number
- CN202510587359.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-08
- Publication Date
- 2025-06-20
AI Technical Summary
When traditional vibration isolation structures face vibration and noise problems in different frequency bands, the band gap frequency is not low enough, the structural mass is heavier, and the relative bandwidth is not large enough, which cannot effectively solve the vibration and noise problem.
Using a medium and low frequency vibration isolation plate based on a phononic crystal structure, a trampoline helical phononic crystal single cell array containing 11 by 11 cylinders is constructed, and a perfect matching layer is added to both sides of it, forming a vibration isolation effect with a large band gap and a relatively large bandwidth.
Effective suppression and isolation of medium and low frequency elastic waves is achieved, the band gap frequency is reduced, and the relative bandwidth is greater than 50%, while reducing the overall structural weight of the vibration isolation plate.
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Figure CN120175779A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a vibration isolation plate, and particularly to a mid-low frequency vibration isolation plate based on a phononic crystal structure. Background Art
[0002] In modern society, vibration and noise are important factors affecting the performance of various devices and the comfort of personnel. Especially in large transportation tools such as ships, the problem of vibration and noise is particularly prominent. With the development of ships towards high speed, large size and light weight, the problem of vibration and noise has become increasingly severe, directly affecting the reliability of equipment and the comfort of personnel. Therefore, modern ship vibration reduction technology has become an important research direction. Current vibration reduction technologies mainly focus on how to reduce vibration through structural design and material selection. However, traditional methods often have difficulty in comprehensively dealing with vibration and noise problems in different frequency bands, resulting in certain limitations in vibration isolation performance. Therefore, traditional vibration isolation structures face challenges such as insufficiently low bandgap frequencies, relatively heavy structural masses, and insufficiently large relative bandwidths, and cannot effectively solve the above problems.
[0003] In recent years, due to its unique mechanical properties, phononic crystals have been widely applied in the field of vibration and noise control. By means of periodic structural design, phononic crystals can form bandgaps in specific frequency bands, thereby effectively suppressing vibration and noise within these frequency bands. Its bandgap mechanisms are mainly divided into two categories. One is the Bragg scattering type, which forms a forbidden band through destructive interference generated by a periodic structure. The other is the local resonance type, which realizes bandgap regulation by relying on the resonance coupling between scatterers and elastic waves.
[0004] This provides a new idea for the control of low-frequency vibration and broadband noise. Especially in the design of ship protection structures, phononic crystals show great application potential. However, an important problem in traditional phononic crystal research is that once fabricated, its structure cannot be adjusted, making it difficult to adapt to bandgap and vibration reduction and noise reduction requirements in different situations, thus limiting its application scope. Summary of the Invention
[0005] Object of the Invention: The object of the present invention is to provide a mid-low frequency vibration isolation plate based on a phononic crystal structure to increase the relative bandwidth, reduce the bandgap frequency and reduce the mass.
[0006] Technical Solution: The mid-low frequency vibration isolation plate described in the present invention includes: a middle phononic crystal, a left excitation region, a leftmost perfectly matched layer, a right protected region, and a rightmost perfectly matched layer; the structure of the middle phononic crystal is formed by an array of 11×11 trampoline spiral phononic crystal unit cells containing cylinders.
[0007] Preferably, the lattice of the phononic crystal unit cell is a hexagonal lattice, a tetragonal lattice or other lattices with symmetry.
[0008] Preferably, the lattice constant of the phononic crystal unit cell is 23 - 32 mm.
[0009] Preferably, the phononic crystal unit cell includes four quarter - cylindrical Archimedean spiral grooves.
[0010] Preferably, the excitation source in the left - hand excitation region includes point load, edge load, specified displacement, and torque.
[0011] Preferably, the part entering the middle phononic crystal from the left - hand excitation region is defined as integration domain 1, and the velocity, acceleration, or kinetic energy of the integration domain 1 is measured.
[0012] Preferably, the left - most perfectly matched layer and the right - most perfectly matched layer are completely matched with the computational domain through wave impedance, and the incident wave enters the perfectly matched layer region at the boundary and decays rapidly.
[0013] Preferably, the part entering the middle phononic crystal from the right - hand protected region is defined as integration domain 2, and the velocity, acceleration, or kinetic energy of the integration domain 2 is measured.
[0014] Preferably, the medium - and low - frequency vibration isolation plate can be made of titanium metal, tungsten, aluminum, high - strength alloy steel, copper, and lead.
[0015] Preferably, the thickness of the medium - and low - frequency vibration isolation plate is 2.6 - 4.6 mm.
[0016] Advantageous effects: Compared with the prior art, the present invention has the following remarkable advantages: introducing a phononic crystal structure and constructing Archimedean spiral grooves, thereby reducing the overall structural weight of the vibration isolation plate, achieving a relative bandwidth greater than 50% and a lower bandgap frequency for medium - and low - frequency elastic waves in the range of 2000 Hz to 3000 Hz, and adding finite - height cylinders to the trampoline spiral phononic crystal structure, effectively solving the problem that the buffering effect of the ship's base plate on the impact force of ocean waves in the prior art is not ideal and easily causing high noise on the ship. Description of the Drawings
[0017] Figure 1 is a schematic diagram of the overall structure of the present invention;
[0018] Figure 2 is a schematic diagram of the structure of the phononic crystal unit cell of the present invention;
[0019] Figure 3 is a schematic diagram of the structure of the middle phononic crystal of the present invention;
[0020] Figure 4 is a schematic diagram of the bandgap structure of the phononic crystal unit cell of the present invention;
[0021] Figure 5 is a schematic diagram of the transmission loss spectrum of the phononic crystal unit cell of the present invention. Detailed implementation mode
[0022] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.
[0023] As Figure 1 shown, the mid-low frequency vibration isolation plate based on the phononic crystal structure includes: the middle phononic crystal 1, the left excitation region 2, the leftmost perfectly matched layer 3, the right protected region 4, and the rightmost perfectly matched layer 5. The mid-low frequency vibration isolation plate can suppress and isolate the vibration caused by mid-low frequency elastic waves or sound waves. The material selected for this vibration isolation plate structure is high-strength alloy steel, which is used to test the propagation of sound waves or elastic waves generated by various excitation sources in the entire vibration isolation plate structure. Its density is 7850 kg / m3, the Young's modulus is 200 GPa, and the Poisson's ratio is 0.3.
[0024] The vibration isolation plate structure is formed by first performing an 11×11 periodic array on the trampoline spiral phononic crystal unit cell structure containing cylinders as the middle phononic crystal structure. Then, square phononic crystal plates with side lengths of 11a (a is the lattice constant) are added on both sides of it, namely the left excitation region 2 and the right protected region 4. Finally, perfectly matched layers 3 and 4 are added on the leftmost and rightmost sides. The mid-low frequency vibration isolation plate with a length of 33a, a width of 11a, and a thickness of the plate thickness is formed through the above process.
[0025] Phononic crystals have their unique bandgap characteristics. Sound waves or elastic waves with frequencies within the bandgap range of the phononic crystal generated by the excitation source are formed and propagate smoothly in the left excitation region, and their propagation is suppressed after entering the middle phononic crystal structure.
[0026] As Figure 2 shown, the main geometric parameters of the phononic crystal unit cell are as follows:
[0027] The plate thickness th = 3.6 mm, the lattice constant a = 25 mm, the groove width w = 0.58 mm, the starting radius rin of the Archimedean spiral = 5.9 mm, the terminating radius r of the Archimedean spiral = 8.1 mm, the radius rx of the cavity cylinder = 7 mm, the radius rh of the additional finite-height cylinder = 4 mm, the height h0 of the additional finite-height cylinder = 24 mm, and the number of turns n of the Archimedean spiral coil (regarded as the ratio of the rotation angle of the Archimedean spiral to 2π) = 0.55.
[0028] The plane Cartesian coordinate parametric equation of the Archimedean spiral is:
[0029]
[0030] Among them, θ represents the polar angle (usually in radians), α represents the polar radius when θ = 0, that is, the inner diameter (initial radius), and β represents the physical quantity that measures the rotational speed of the equiangular spiral, which is usually defined as the increase (or decrease) amount of the polar radius when rotating 1 rad.
[0031] The left excitation region 2 refers to a square plate with a side length of 11a on the left side of the overall structure. Usually, an excitation source is placed in this region, and a part with a width of a and a length of 11a where the left excitation region 2 is about to enter the middle phononic crystal 1 structure is defined as the integration domain 1, used to measure the velocity, acceleration, or kinetic energy of this integration domain. The right protected region 4 refers to a square plate with a side length of 11a on the right side of the overall structure, and a part with a width of a and a length of 11a where the right protected region 4 is about to enter the middle phononic crystal 2 structure is defined as the integration domain 2, used to measure the velocity, acceleration, or kinetic energy of this integration domain.
[0032] To quantitatively measure the vibration isolation characteristics of the designed phononic crystal structure, the velocity, acceleration, or kinetic energy in the two regions are measured through the integration domain 1 and the integration domain 2, and the definition of transmission loss is introduced:
[0033] TL1 = 20×lg(a out / a in );
[0034] TL2 = 20×lg(W k,out / W k,in );
[0035] Among them, a out and a in are the vertical acceleration amplitudes of the right protected region and the left excitation region respectively, while W k,out and W k,in are the kinetic energies of the right protected region 4 and the left excitation region 2 respectively. When a out <a in or W k,out <W k,in , the transmission loss is negative, indicating that the energy of the sound wave or elastic wave has attenuated, and the suppression of its propagation has been successfully achieved.
[0036] The leftmost perfectly matched layer 3 and the rightmost perfectly matched layer 5 are an artificially designed absorbing boundary condition, mainly used to efficiently absorb the outgoing wave in numerical simulations (such as the finite element method), thereby avoiding the influence of boundary reflection on the calculation results. Its core feature is that the wave impedance is completely matched with the computational domain, so that the incident wave enters the perfectly matched layer region with almost no reflection at the boundary and decays rapidly.
[0037] The trampoline spiral phononic crystal unit cell structure containing a finite-height cylinder has a large mid-low frequency bandgap, and the bandgap range is 1807 Hz - 3019.9 Hz, as Figure 4As shown. Elastic waves are a type of stress waves. Generally, it refers to the process in which particles in an elastic medium deviate from the equilibrium position to generate strain, vibrate under the action of elastic restoring force, and trigger the chain vibration of adjacent particles, thus forming a wave propagation process, and the wave vibration direction is perpendicular to the wave propagation direction. The relative bandwidth is an important parameter for measuring the quality of the phononic crystal bandgap, and its definition is as follows:
[0038] f RBW = 2(f H - f L ) / (f H + f L );
[0039] Among them, f H and f L respectively represent the upper limit and the lower limit of the bandgap. The introduction of the relative bandwidth quantitatively measures the size of the bandgap width and the low-frequency degree of the bandgap. The larger this value is, the larger the bandwidth or the more the bandgap tends to be low-frequency.
[0040] Figure 5 This is the transmission spectrum (transmission loss spectrum) of the structure of the present invention. It can be seen that the transmittance in a frequency band of the transmission spectrum is very low, and elastic waves can hardly penetrate this phononic crystal structure, and this frequency range just corresponds to the cut-off frequency and the starting frequency of the bandgap in the energy band structure diagram, which verifies that the entire phononic crystal structure cannot be penetrated by sound waves / elastic waves within the bandgap range.
[0041] The trampoline spiral phononic crystal structure containing finite-height cylinders based on high-strength alloy steel has an elastic wave or acoustic wave bandgap in the medium and low frequencies. On the basis of not affecting the structural strength, the designed unit cell structure generates a large bandgap at a lower frequency, and the relative bandwidth reaches 50%, which is of great significance for realizing a new generation of phononic crystal vibration isolation structures with medium and low frequencies and light weight.
Claims
1. A medium and low frequency vibration isolation plate based on a phononic crystal structure, characterized in that: include: A middle phononic crystal (1), a left excitation zone (2), a leftmost perfect matching layer (3), a right protected zone (4) and a rightmost perfect matching layer (5); the structure of the middle phononic crystal (1) is formed by an 11 by 11 trampoline spiral phononic crystal unit cell array containing cylinders.
2. The vibration isolation plate according to claim 1, characterized in that: The lattice of the phononic crystal unit cell is a hexagonal lattice, a tetragonal lattice or other lattices with symmetry.
3. The vibration isolation plate according to claim 2, characterized in that: The lattice constant of the phononic crystal unit cell is 23-32 mm.
4. The vibration isolation plate according to claim 2, characterized in that: The phononic crystal unit cell comprises four quarter-cylindrical Archimedean spiral grooves.
5. The vibration isolation plate according to claim 1, characterized in that: The excitation sources of the left excitation area (2) include point loads, edge loads, specified displacements, and torques.
6. The vibration isolation plate according to claim 1, characterized in that: The portion from the left excitation region (2) into the middle phononic crystal (1) is defined as an integration domain 1, and the velocity, acceleration or kinetic energy of the integration domain 1 is measured.
7. The vibration isolation plate according to claim 1, characterized in that: The leftmost perfect matching layer (3) and the rightmost perfect matching layer (5) are completely matched with the calculation domain through wave impedance, and the incident wave enters the perfect matching layer region at the boundary and decays rapidly.
8. The vibration isolation plate according to claim 1, characterized in that: The portion from the right protected area (4) into the middle phononic crystal (1) is defined as an integration domain 2, and the velocity, acceleration or kinetic energy of the integration domain 2 is measured.
9. The vibration isolation plate according to claim 1, characterized in that: The medium and low frequency vibration isolation plates may be made of titanium, tungsten, aluminum, high strength alloy steel, copper and lead.
10. The vibration isolation plate according to claim 1, characterized in that: The thickness of the medium and low frequency vibration isolation plate is 2.6-4.6 mm.