Efficient Optimization Procedure For Minimizing Vibratory Response Via Redesign Or Modification, Part II: Examples

Abstract By using an optimization method presented in the companion paper, Part I, the optimal structural modifications leading to minimization of the vibratory response are found. A number of examples are given in this paper, from simple spring-mass systems to continuous finite element models of beams and plates. The application of the method for various cases provides illuminating results. As shown, one is able to attach engineering common sense to these solutions, in some cases, and to obtain insight about the nature of a dynamically optimal structure. Most results are interpreted by using frequency response functions, where the resulting modified structural resonance and anti-resonance frequencies, or the mode shapes, tend to behave in a special way related to the excitation and boundary conditions. The geometry of the optimized structure, as demonstrated in the paper, reflects the boundary conditions and force location. Some similarities between the optimized shape, resulting from a "dynamic" optimization, with shapes obtained by prior investigations dealing with only static deflections, can be noted. An experimental verification showing a simple case of point masses added to a vibrating beam shows good agreement of theory with the experimental results.