CN-122021000-A - Lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method

CN122021000ACN 122021000 ACN122021000 ACN 122021000ACN-122021000-A

Abstract

The application provides a lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method, which belongs to the technical field of acoustic black hole vibration reduction and isolation, and establishes an acoustic black hole designed lattice structure according to an acoustic black hole design principle and the relation between lattice cell structure variables and equivalent rigidity; according to the application, the acoustic black hole lattice in a continuum form is not locally designed in the design process, but dynamic homogenization equivalent is carried out on each cell by a mechanical equivalent method, so that the acoustic black hole design is realized on the whole structure level, the phenomenon of local damage in the acoustic black hole structure in the cell in the prior art is solved, and the requirement of reducing the influence of external excitation of the lattice structure on the normal use of the structure in a complex vibration environment is met.

Inventors

DUAN CHENGYU
YE BIN
WANG PANDING
ZHAO ZEANG
LEI HONGSHUAI

Assignees

北京理工大学

Dates

Publication Date: 20260512
Application Date: 20260119

Claims (10)

1. The integral acoustic black hole vibration reduction and isolation design method for the lattice structure is characterized by comprising the following steps of: S1, according to an Euler-Bernoulli beam theory, a lattice sandwich beam is equivalent to be discrete Liang Moxing, an integral acoustic black hole design principle based on an equivalent beam model is derived, and an equivalent beam unit in the beam model is replaced with a lattice cell with equivalent specific stiffness meeting the requirement; determining geometric design variables and variation ranges of cells, and carrying out dynamic homogenization calculation on lattice cells; S2, establishing a lattice structure of the acoustic black hole design according to the acoustic black hole design principle and the relation between lattice cell structural variables and equivalent rigidity; S3, assembling in modeling software; s4, manufacturing a finished product (100) according to modeling software.
2. The lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method according to claim 1, wherein in S1, according to the euler-bernoulli beam theory, a motion control equation of a beam model is: Wherein, the , For the length of the unit cell, And Is a beam at Young's modulus and density at; The displacement is set to be in a simple harmonic wave general solution form Substituting the motion equation, Time, simultaneously let the external force term At zero, the resulting characteristic equation is: 。
3. The lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method according to claim 2, wherein in S1, the frequency is as follows And wave number The relation is: 。
4. The lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method according to claim 3, wherein in S1, the wave propagation time in the beam structure is Group velocity Satisfy the following requirements The propagation time is therefore: Wherein, the The method is marked as equivalent specific stiffness, combines a continuum acoustic black hole design principle, leads the propagation time of the wave in the equivalent beam model obtained by the method to tend to be infinite, and obtains the overall acoustic black hole design principle as follows: Wherein, the Is a scalar parameter; And deducing an overall acoustic black hole design principle based on an equivalent beam model, and replacing an equivalent beam unit in the beam model with a lattice cell with equivalent specific stiffness meeting the requirement.
5. The method for designing the vibration isolation and reduction of the integral acoustic black hole facing the lattice structure according to any one of claims 1to 4, wherein in S1, the required lattice cell type is selected, the geometric parameters such as the rod radius or the panel thickness are determined as design variables, and the variation range of the variables with reasonable design is determined as a design domain.
6. The lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method according to claim 5, wherein in S1, floquet type periodic boundary condition setting is carried out on cells to complete dynamic homogenization, so that equivalent specific stiffness of lattice cells under corresponding geometric structure parameters is obtained.
7. The lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method according to claim 6, wherein in S1, the original design principle based on the equivalent beam unit model is rewritten into the following discrete form: Wherein, the , Respectively the cell sequence number and the total number of cells, And And selecting corresponding geometric structure parameters from corresponding cell serial numbers by combining the discrete form and the proxy model of the established cell specific rigidity with respect to the structural parameters to establish lattice cells.
8. The lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method according to claim 1, wherein in the step S4, a 3D printing mode is adopted for manufacturing.
9. The lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method according to claim 1, further comprising the steps of: S5, carrying out mechanical analysis, and carrying out mechanical analysis on the finished product (100) manufactured in the step S4.
10. The method for designing the vibration reduction and isolation of the integral acoustic black hole facing the lattice structure according to claim 9, wherein in S5, solid blocks (110) are respectively assembled at both ends of the finished product (100) to facilitate the clamping and the detection of the displacement amplitude.

Description

Lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method Technical Field The invention relates to the technical field of acoustic black hole vibration reduction and isolation, in particular to an integral acoustic black hole vibration reduction and isolation design method for a lattice structure. Background The material of the lattice structure is an ordered porous structure, the density of the material is far lower than that of a solid structure made of the same material, the material has good specific stiffness, bending resistance and heat dissipation performance, and the material has a large application space in the fields of construction, ships, vehicles and aerospace. When the lattice structure encounters sound waves or elastic waves, a frequency forbidden band can appear, so that the sound waves or elastic waves in specific frequency bands cannot be transmitted, and the lattice structure has good vibration reduction and sound insulation performances. The traditional lattice structure has strong bearing capacity, but heavy weight, and the forbidden band characteristic is mostly concentrated in medium and high frequency, but the vibration reduction and noise reduction effects for medium and low frequency are poor. At present, an acoustic black hole area adhered with a damping layer exists in each unit cell of the sandwich board, so that energy brought by vibration is gathered in the area and dissipated, vibration of a lattice structure is reduced, vibration reduction and isolation effects are effectively improved, for example, a novel lattice sandwich board based on the acoustic black holes and a manufacturing method thereof are disclosed in China patent No. CN114619726A, a certain problem exists in the prior art, and the lattice sandwich board with the continuous acoustic black holes uniformly distributed in each unit has an inverse relation with the thickness of the structure due to the vibration amplitude of the structure in the vibration process, namely, the energy is gathered at the position with smaller thickness. This characteristic will directly lead to local damage in the acoustic black hole structure within the cell, thereby affecting the safety performance of the overall structure. Therefore, a new technical solution is needed to solve the above-mentioned design method for reducing vibration isolation of the whole acoustic black hole. Disclosure of Invention Therefore, the invention aims to overcome the defect that the local damage phenomenon occurs in the acoustic black hole structure in the unit in the prior art, thereby providing the integral acoustic black hole vibration reduction and isolation design method for the lattice structure. The invention provides a lattice structure-oriented integral acoustic black hole vibration reduction and isolation design method, which comprises the following steps: s1, according to an Euler-Bernoulli beam theory, a lattice sandwich beam is equivalent to a discrete beam model, and an overall acoustic black hole design principle based on the equivalent beam model is deduced, so that an equivalent beam unit in the beam model can be replaced with a lattice cell with equivalent specific stiffness meeting the requirement; determining geometric design variables and variation ranges of cells, and carrying out dynamic homogenization calculation on lattice cells; S2, establishing a lattice structure of the acoustic black hole design according to the acoustic black hole design principle and the relation between lattice cell structural variables and equivalent rigidity; S3, assembling in modeling software; S4, manufacturing according to modeling software. In one possible embodiment, in S1, the motion control equation of the beam model is known from euler-bernoulli beam theory as follows: Wherein, the ,For the length of the unit cell,AndIs a beam atYoung's modulus and density at; Is the thickness of the beam. Let displacement be a simple harmonic wave general solution Substituting the motion equation,Time, simultaneously let the external force termThe zero-availability characteristic equation is: 。 In one possible embodiment, in S1, the frequency And wave numberThe relation is: 。 In one possible embodiment, in S1, the wave travel time within the beam structure may be written as Group velocitySatisfy the following requirementsThe propagation time can therefore be written as: Wherein, the The method is marked as equivalent specific stiffness, combines a continuum acoustic black hole design principle, leads the propagation time of the wave in the equivalent beam model obtained by the method to be infinite, and can obtain the overall acoustic black hole design principle as follows: Wherein, the Is a scalar parameter; And deducing the design principle of the whole acoustic black hole based on the equivalent beam model, and replacing the equivalent beam unit in the beam model into a lattice cell with equivalent specific stif