Design of graded piezoelectric metamaterial beam with spatial variation of electrodes

Abstract

This work presents a novel strategy of broadband vibration attenuation using a graded piezoelectric metamaterial beam. A series of electrode pairs with varying lengths are applied to the fully covered piezoelectric beam, and each electrode pair is connected to an identical shunt resonant circuit. Unlike the existing grading strategies, which normally consider the varying material properties of local resonators, the proposed graded metamaterial enables us to broaden the vibration attenuation region through varying spatial profiles. In this paper, the graded metamaterial beam is modeled analytically and verified by finite element. Subsequently, an analytical expression is derived to predict the “aggregated” gap region with graded electrodes. A parametric study on the transmittance response reveals that the increase of spatial variation of electrodes contributes to widening the attenuation region while weakening the attenuation strength. An optimization strategy aiming to enhance the overall attenuation performance is given, through which the graded piezoelectric metamaterial beam exhibits significant superiority over a non-graded one in terms of average transmittance. Further, an example shows that the damping induced by the load resistance in the shunt resonant circuit can dramatically reduce the resonant peaks inside the “aggregated” gap. With a properly selected resistance, a theoretical widest attenuation region is achieved by using the graded piezoelectric metamaterial beam, with 289.2% increase in the bandwidth as compared to the conventional one. This study differentiates itself as a powerful alternative to other grading strategies for realizing broadband vibration attenuation.