Non-parametric free-form optimization of shell structures for reducing the sound pressure in a closed space

Abstract

This paper describes a parameter-free free-form optimization method for shell structures to reduce the noise in a closed acoustic field. Squared sound pressure, which is evaluated by solving fully coupled shell-acoustic interaction system, is selected as the objective function to be minimized. The optimum design problem is formulated as a distributed-parameter shape optimization problem under the assumptions that shell structures are varied in the out-of-plane direction to the surface and the thickness is constant. The shape gradient function and the optimality conditions are derived by using the material derivative method, and they are applied to the free-form optimization method for shells. The shape gradient function is applied to the shell surface as a fictitious distributed force under Robin condition for varying the surface, for minimizing the objective functional and for regularizing the mesh. With this method, the smooth optimal free-form of shell structures are obtained without any shape design parameterization. The validity of this method for the radiated noise reduction from vibrating shell structures in a closed space is verified through design examples.