Shape Optimization on Acoustic-Structure Interaction Problems

This paper presents a numerical method for solving nonparametric boundary shape optimization problems of acoustic-structure interaction problems. Weak form of the acoustic-structure interaction problem considering strong coupling is presented and used as state equations for the shape optimization problem. Sound pressure power integral in a sub-domain included in the acoustic field during frequencies of interest is chosen as an objective functional. Evaluation method of the shape gradient of the objective functional with respect to domain variation is derived theoretically by the adjoint variable method and the Lagrange multiplier method. Based on the shape gradient, a traction method proposed by Azegami and coworkers is applied for reshaping algorithm maintaining smoothness of the boundary shape. The validity of the solution is confirmed by numerical example for a box model made of linear elastic material surrounding a acoustic field