An objective function for the topology optimization of sound-absorbing materials

We propose a new objective function for optimizing a sound-absorbing material layout. The optimization seeks to reduce the average pressure of the domain in the resonance state. The properties of the sound-absorbing material were modeled as an equivalent fluid. The propagation of sound under periodic accelerations was treated using the Helmholtz equation. The energy loss through the sound-absorbing material was found and used as an objective function, which we refer to as the sound dynamic compliance. The topology optimization was implemented using the solid isotropic material with penalization (SIMP) method. The optimization problem involved maximizing the imaginary part of the sound dynamic compliance under a volume constraint. Quasi-1D and 3D numerical examples were presented to illustrate the validity and utility of the proposed method over the conventional straightforward pressure reduction optimization. Whereas no suitable solution that reduces the resonance peak was obtained using the conventional approach for some frequency inputs, the proposed approach obtained such solutions and generated optimal results for each example exhibiting high robustness against input frequency.