Abstract

This paper is concerned with the shape optimization of structures to attain prescribed normal mode shapes. Optimizing structural members in order to have desired mode shapes, besides the desired natural frequencies, is of interest in some applications at both macro and micro scales. After reviewing the relevant past work on the “inverse mode shape” problem, a feasibility study using the lumped spring-mass models and finite element models of an axially vibrating bar is presented. Based on the observations made in the feasibility study with bars, a meaningful optimization problem is formulated and solved. Using finite element analysis and numerical optimization, a method for designing beam-like structures for prescribed mode shapes is developed. The method is demonstrated with an example of designing the cross-sectional area profile of a beam along its longitudinal axis to get a desired fundamental mode shape. The nonuniqueness of the solution is noted and avenues for future research are identified.

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