Wave Motion Optimization in Periodically Distributed Shunted Piezocomposite Beam Structures

Abstract

This article proposes a new, simple, and efficient strategy, allowing one to optimize the diffusion operator between a passive beam coupled to a like beam equipped with a periodically distributed network of shunted piezoelectric patch actuators. A multimodal wave dispersion model is used to compute the diffusion operator and analyze the stability properties of the combined system. Based on this mathematical tool, specific optimization procedures are introduced to allow maximization or minimization of the wave transmissibility between the passive and the active distributed beam. A specific example is used to demonstrate the capability of the shunted piezoelectric system to induce total reflection through the total absorption of incoming propagating flexural waves while guaranteeing the stability, robustness, and realizability of such a system.