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Topology optimization with multiple materials studies were commonly adopted to address the issues of complex structures and dynamic loading cases. However, the perturbation excited from the transient load will be propagated and change the local stress level in the structure. Therefore, it is indispensable to consider impedance mismatching of waves at the interfaces of multi-materials layers in the optimization model. In this work, the wave impedance will be regarded as constraint conditions and assessment indicators in the optimization design. Firstly, a multi-material interpolation model using SIMP models is established based on the variable density method. Secondly, the optimization process is applied by combining using Newmark-Formula: see text method which is used to solve the dynamic response, an adjoint variable method for sensitivity study, and an optimization criterion method employed to update the design variables. Finally, the simulation examples are used to analyze the influence of impedance mismatching and volume fraction for multilayer dielectric on response. The results indicate that the position and content of the Polymethyl Methacrylate (PMMA) plays a key role in reducing vibration and buffering action.
Zhang et al. (Fri,) studied this question.