Tailoring vibration mode shapes using topology optimization and functionally gradedmaterial concepts

Abstract

Tailoring specified vibration modes is a requirement for designing piezoelectric devicesaimed at dynamic-type applications. A technique for designing the shape of specifiedvibration modes is the topology optimization method (TOM) which finds an optimummaterial distribution inside a design domain to obtain a structure that vibrates accordingto specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied todynamic problems, the well-known grayscale or intermediate material problem arises whichcan invalidate the post-processing of the optimal result. Thus, a more natural way forsolving dynamic problems using TOM is to allow intermediate material values. This idealeads to the functionally graded material (FGM) concept. In fact, FGMs are materialswhose properties and microstructure continuously change along a specific direction.Therefore, in this paper, an approach is presented for tailoring user-defined vibrationmodes, by applying the TOM and FGM concepts to design functionally gradedpiezoelectric transducers (FGPT) and non-piezoelectric structures (functionally gradedstructures—FGS) in order to achieve maximum and/or minimum vibration amplitudes atcertain points of the structure, by simultaneously finding the topology and materialgradation function. The optimization problem is solved by using sequential linearprogramming. Two-dimensional results are presented to illustrate the method.