On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation

Abstract

This work deals with the topological design of vibrating continuum structures. The vibration of continuum structure is excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. In comparison with well-known compliance minimization in static topology optimization, various objective functions are proposed in literature to minimize the response of vibrating structures, such as power flow, vibration transmission, and dynamic compliances, etc. Even for the dynamic compliance, different definitions are found in literature, which have quite different formulations and influences on the optimization results. The aim of this paper is to provide a comparison of these different objective functions and propose reference forms of objective functions for design optimization of vibration problems. Analytical solutions for two degrees of freedom system and topological design of plane structures in numerical examples are compared using different optimization formulations for given various excitation frequencies. The results are obtained by the finite element method and gradient based optimization using analytical sensitivity analysis. The optimized topologies and vibration response of the optimized structures are presented. The influence of excitation frequencies and the eigenfrequencies of the structure are discussed in the numerical examples.