Sensitivity Analysis and Shape Optimization of a Hole in a Vibrating Rectangular Plate for Eigenfrequency Maximization

Abstract

A hole inside a rectangular thin plate is optimized for maximization of an eigenfrequency of the structure. The shape of the hole is represented by an ellipse parametrization to guarantee a smooth curve along the boundary; and the hole’s center position, semiaxes, and rotation are treated as shape design variables. The Rayleigh-Ritz approach is applied to constitute the vibration frequency equation such that an exact procedure can be presented for the frequency sensitivity analysis. The hole shape optimization is performed by using a combined mathematical programming algorithm with different search directions for two sets of design variables in relation to the constraint of the hole’s size. In addition, a simple optimality criterion is provided for the optimum profile design of the internal hole of a given area. Several illustrative examples demonstrate the validity and effectiveness of the design sensitivity analysis and the proposed optimization method.