An investigation of optimal non-uniform locally resonant piezoelectric metamaterials

Abstract

Locally resonant metamaterials are capable of producing frequency attenuation regions that are not dependent on the lattice size and have been object of several studies since the 2000s. Most recently, flexible structures with periodically distributed piezoelectric attachments combined to resonant circuits have been studied as locally resonant piezoelectric metamaterials. In this work the authors use a genetic algorithm to optimize each unit cell of a piezoelectric metamaterial in order to obtain wider attenuation bands. An assumed-modes solution for a piezoelectric bimorph beam with segmented electrodes under transverse vibrations is presented. Although the unit cells of the optimized configurations have the same length (periodically distributed along the length), the target frequency of each cell varies, leading to optimal non-uniform configurations that exhibit wider attenuation bands than the uniform ones. The optimization of the proposed objective function converges to a non-uniform configuration that displays an attenuation band 56% wider than the reference case.