Thickness optimization of a multilayered structure on the coupling surface between a structure and an acoustic cavity

This paper describes a new design method to optimize thickness distribution of a multilayered structure which is located on the coupling surface between a structure and an acoustic cavity. The design method is based on the concept of the density approach in topology optimization incorporating a transfer matrix for a multilayered structure that includes a poroelastic media layer. The one-dimensional transfer matrix adopted here is an approximate representation addressing vibro-acoustic effects inherent in a multilayered structure, and balances calculation resources and desired accuracy. Applying the transfer matrix representation as boundary conditions on the coupling surface between a structure and an acoustic cavity, the modified equilibrium equation of the vibro-acoustic system is derived which is approximately but efficiently solved by the modal approach. In this study, the problem of minimizing the acoustic pressure within the cavity over the prescribed frequency range is formulated under the volume constraint of the poroelastic media layer. The continuous approximation of thickness distribution is assumed, and the thickness of the poroelastic media layer at each nodal point is chosen as design variables. Numerical results show that an acoustic response is significantly reduced by the optimal thickness distribution having a total weight equal to or less than that in the initial uniform thickness. These demonstrate that the proposed method is effective to design the optimal thickness distribution of a multilayered structure.