Evolutionary topology optimization for natural frequency maximization problems considering acoustic–structure interaction

• Topology optimization is applied to natural frequency maximization problems.
• A displacement/pressure formulation is used to analyze coupled systems.
• The proposed optimization procedure is based on the BESO method.
• The objective is to maximize natural frequencies of the coupled systems.

This paper aims to extend the evolutionary methods of topology optimization to free vibration problems of acoustic–structure systems. The interacting fluid and structure fields are governed by the acoustic wave equation and the linear elasticity, respectively. Both domains are solved with the finite element method. The coupling conditions are the equilibrium and kinematic compatibility at the acoustic–structure interfaces. The proposed bi-directional evolutionary structural optimization (BESO) method seeks to maximize the first natural frequencies of the acoustic-structural model by switching elements into solid, fluid or void condition. It allows the acoustic–structure boundaries to be modeled and modified straightforwardly, addressing design-dependent loads on the topology optimization problem with simple finite element formulations. The proposed methodology extension is justified by various possible applications to free vibration of acoustic–structure systems such as tanks/reservoirs, acoustic-structural devices, passengers compartments in automobiles and aircrafts and pipelines. Numerical results show that the evolutionary methods can be applied to this kind of multiphysics problem effectively and efficiently.