The Two-scale Topological Optimization Design And Application Of Vibration And Noise Reduction Properties Of Structure Based On Elastic Metamaterials

In the field of ship engineering,researchers pay more and more attention to suppressing low-frequency vibration and noise.The elastic wave propagation in periodic acoustic metamaterial structure has the characteristic of the band gap.This special property provides a new way for the design of vibration and noise reduction.However,the design of artificial periodic elastic materials is based on the fixed material distribution form in previous studies.The geometric topology configuration of the structure does not change during the optimization process,and the single-cell structure is confined to the fixed shape range.In this paper,a topological optimization method is introduced to directly optimize the material distribution through combining it with the two-scale periodic structure theory,aiming at obtaining the optimal geometric configuration that can improve the capacity of vibration and noise reduction.This paper mainly carried out the following research contents:Topology optimization design of micro-structure is proposed,based on sound absorption characteristics of the periodic acoustic metamaterial structure.First,combined with the finite element method and periodic boundary condition the numerical model is established to solve the covering layer of the sound absorption coefficient.Then,through the method of artificial density topology optimization,the relative density of each element in the viscoelastic material layer design domain as design variables to establish the optimization model with objectives maximizing the frequency point and frequency sound absorption ability.The sensitivity of objective function on design variables was deduced.Numerical examples show that topological optimization improves the low frequency and wide band sound absorption capacity of the overburden structure.Besides,the sound absorption mechanism of the optimized configuration is discussed,and it is found that the structural resonance causes the dissipation of the incident sound energy of the damping material,which is the cause of the sound absorption peak.A micro-scale two-scale topology optimization design for periodic acoustic metamaterial structure with sound absorption performance is presented under specific frequency.When the plate of acoustic metamaterial is excited with a certain frequency,the plate is divided into different macroscopic regions according to the different responses and a specific microstructural unit-cell is designed.A classification criterion was designed,and the Heaviside unit step function was introduced as a punishment function to identify a specific unit-cell structure in a specific region.The results are compared with the acoustic metamaterials plate with the same unit-cell structure,and the numerical results show that the two-scale topological optimization can obtain the materials with better sound absorption.Taking an actual gear box as an object,the above acoustic metamaterial is laid to perform the vibration and noise reduction,and the sound absorption effect of this design is verified.Multi-body dynamics analysis is conducted for the gear box to obtain the gear mesh force and the bearing of the reaction,which is applied as the input loads of vibration characteristic simulation analysis.Under both cases with or without laying acoustic metamaterial respectively,the gearbox vibration characteristic and radiated noise are analyzed.The comparison of the results,verify that the feasibility of the sound absorption effect of the periodic acoustic metamaterial structure.Considering the existing experimental environment,a vibration and noise test platform was built to verify the vibration and noise reduction effect of the periodic acoustic metamaterial structure based on the existing machine tool spindle box.Also,the method of laying constrained damping layer is adopted as a reference.Comparing the noise reduction effect of acoustic metamaterials and constrained damping layer,it is found that the effect of the new elastic metamaterials on vibration and noise suppression is better than that of the constrained damping layer.