Concurrent multi-scale and multi-material topological optimization of vibro-acoustic structures

Abstract

Most of the presented works in the field of vibro-acoustic topology optimization are focused on single-scale design of the structure or material so far, which cannot exert the potential of the material to the largest extent. Even though multi-scale topology optimization has been investigated increasingly in recent years, few works concern the topological design with respect to the vibro-acoustic criteria. In this paper, a concurrent multi-scale multi-material topology optimization method is presented for minimizing sound radiation power of the vibrating structure subjected to harmonic loading. The metamaterial consisting of different periodic microstructures and its distribution over the macrostructural domain are designable to reduce the sound radiation power. A general multi-scale multi-material interpolation model based on SIMP and PAMP is developed and applied to the concurrent topological design. The optimum distribution of the base materials at micro-scale and metamaterial associated with the optimized microstructures at macro-scale will be obtained concurrently. The homogenization method is employed to calculate the equivalent macro-scale material properties of the periodic microstructures. A high-frequency approximation formulation is introduced to simplify calculation of the sound power from the vibrating structure to its surrounding acoustic medium. The sensitivities of the sound power with respect to macro-scale and micro-scale topological densities are calculated by the adjoint method. The MMA method is employed to find the solution of the concurrent multi-scale vibro-acoustic topology optimization problem. Numerical examples are given to validate the accuracy of the established model and show the advantages of the multi-scale topology optimization in specific cases of vibro-acoustic design. Many interesting features of the concurrent vibro-acoustic multi-scale topological design have been revealed and discussed. In comparison with the single-scale microstructural design, the importance of simultaneous macro-structural level design to improve overall vibro-acoustic characteristics of the structure is proved by the examples.