Topology Optimization Of Free-layer Damping Structures For Vibration And Acoustic Response

Thin-wall structures are widely used in the automotive,aerospace and marine industries.In the cavity such as the interior space of vehicle,aircraft cabins and ship cabins,thin wall structures vibrate and cause the medium in the cavity to compress and stretch,causing the sound waves to propagate in the medium,and the structure is also subjected to the reaction force of the sound field in the medium.This is called structural-acoustic coupled system.The free damping structure where pasting a layer of damping material on the surface of the thin-wall structure,can effectively suppress structural vibration and noise,but increase the structural weight and production cost.In order to realize the light weight and ensure the vibration suppression and noise reduction of the damping material in the damping structural-acoustic coupled system,the topology optimization method is applied to obtain the optimal layout of the damping material in the free damping structure.In this thesis,the numerical filtering technique of density-based topology optimization method is studied,and a density filtering method based on density gradient is proposed.The multi-modal loss factor is constructed,and the topology optimization of free damping structure in a frequency range targeting on vibration suppression is realized.Based on the hybrid finite element-wave based method,the topology optimization method of free damping structural-acoustic coupled system with the acoustic response of the coupled system as the optimization target is studied.Based on the density filtering method in the density-based topology optimization method,a density filtering method based on density gradient is proposed.A weighting function containing the information of the relative density gradient is utilized to modify the filter results at the structural boundary that is identified by density gradient,to suppresses the grey scale elements in the optimization results,and accelerates the convergence of the optimization problem.The influence of optimization parameters on the optimization results is analyzed by numerical simulation.Compared with other density filters,the proposed method obtains clear topology optimization results and improves the optimization efficiency.According to the constitutive relation and energy method of free damping plate structures,the finite element model of free damping plate is established,and is verified by experimental results.The effective model mass of the free damping plate is derived.The effective modal mass ratio is applied to construct the multi-modal loss factor to describe the energy dissipation capacity of the structure damping in a certain frequency range.The topology optimization model of the free damping plate is constructed,and the modified density filtering based on density gradient is used to optimize the layout of damping material.The numerical simulation results show that the modified density filtering method based on density gradient correction basically suppresses the grey scale element in the optimization result,and reduces the number of iteration steps.Compared with the optimization result targeting on maxing the modal loss factor,optimized free damping plate achieves good damping effect in a certain frequency range when the multi-modal loss factor is used as the objective function.In the topology optimization of the free damping structural-acoustic coupled system,the finite element model of the design domain(free damping plate),and the wave based model of the non-design domain(sound field)are established,considering the few freedom and high precision of wave based method.The computational accuracy and convergence of the hybrid finite element-wave based method are verified by numerical simulation.Based on the low and mid frequency acoustic response of the coupled system as the objective function,the topology optimization model of the free damping structural-acoustic coupled system under harmonic excitation is constructed.The adjoint sensitivity method is used to derive the sensitivity of sound pressure response to the design variables.The results of simulation and experiment show that the optimized damping material layout can reduce the sound pressure at the target frequency effectively.The coupled system topology optimization results based on the hybrid finite element-wave function model are consistent with the results based on the finite element model with higher optimization efficiency.