Shape Optimization Analysis for Frequency Response Problems of Solids with Proportional Viscous Damping

摘要

The purpose of this paper is to present a numerical method of shape optimization for the frequency response problems of solids with proportional viscous damping. We treat the minimization problems of the strain energy, the kinetic energy and the absolute value of mean compliance. The objective functions are expressed in terms of displacement vector and its conjugate complex number, and the state equation is written in continuum form. We derive the shape gradient functions using material derivative formula and the Lagrange multiplier method, and calculate the adjoint variables using modal parameters. The traction method is applied for numerical analysis. Numerical examples of beam-like plate problems are given to show the validity of this approach.