Interface Shape Optimization for Controlling Natural Frequency of Composite Structure

Abstract

In this paper, a non-parametric shape optimization method is proposed for designing the interface and the outer boundary shapes of a three dimensional composite structure composed of dissimilar materials in natural vibration problem. We employ a squared error norm to a target eigenvalue as the objective functional to be minimized. The shape gradient function is derived using the Lagrange multiplier method, the adjoint variable method and the material derivative method, and is applied to shape update based on the H¹ gradient method. The specified mode is traced using the MAC value. The method is applied to several design examples, and the results show that the proposed method can successfully control the vibration eigenvalue to the target, while maintaining the smoothness of the design boundaries.