Structural design for desired eigenfrequencies and mode shapes using topology optimization

A technique is proposed for determining the material distribution of a structure to obtain desired eigenmode shapes for problems of maximizing the fundamental eigenfrequency. The design objective is achieved using the solid isotropic method with penalization (SIMP) for topology optimization. Weighted constraints added in bound formulation are proposed to maximize the fundamental natural frequency, which provides an easy and straightforward way to prevent mode switching in the optimization process. Aside from maximizing the fundamental frequency, a method to modify existing eigenmodes to continuously evolve and assume the same shapes as the desired modes within the optimization process is proposed. The topology layout of a structure with desired eigenmodes is obtained by adding the modal assurance criterion (MAC) as additional constraints in the bound formulation optimization. Examples are presented to illustrate the proposed method, and a potential application of the proposed technique in decoupling a mechanical system is demonstrated.