Level set based topology optimization of vibrating structures for coupled acoustic–structural dynamics

•A level set based topology optimization for coupled structural-acoustic structures.•A sensitivity analysis with respect to the structural boundary variations.•Numerical algorithm using material derivative and the adjoint method.•Examples of optimal structures of the coupled structural-acoustic system with smooth boundary.

A level set based structural topology optimization method is proposed for the optimal design of coupled structural–acoustic system with a focus on interior noise reduction. The objective is to consider an optimum structure with an optimum interface between the structural and acoustic domains, for minimizing the acoustic response of the coupled system at specified points or surfaces inside the acoustic domain within a frequency range of interest, subject to the given amount of the material of the structure. A sensitivity analysis with respect to the structural boundary variations is carried out using material derivative and the adjoint method, while the standard finite element method is employed for solving the state equation and the adjoint equation. The optimal structure of the coupled structural–acoustic system with smooth boundary is obtained through the level set evolution, while the velocity field is derived from the sensitivity analysis and the optimization algorithm. A number of numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed approach for the noise reduction purpose.