Topological Properties and Localized Vibration Modes in Quasiperiodic Metamaterials With Electromechanical Local Resonators

Abstract

Abstract Simultaneous energy harvesting and vibration attenuation has been a topic of great interest in many recent investigations in mechanical metamaterials. These studies have shown the ability to harvest electrical power using weak electromechanical coupling in periodic metamaterials with no effect on the material’s bandgap boundaries. However, the effect of the electromechanical resonator on the topological properties (i.e. the bandgap topology) and localized mode shapes of a quasiperiodic metamaterial has not yet been determined. In this paper, we study a quasiperiodic metamaterial coupled to electromechanical resonators to observe its bandgaps and localized vibration modes. We show here the analytical dispersion surfaces of an infinite quasiperiodic metamaterial with electromechanical local resonators. The natural frequencies of a semi-infinite system are also simulated numerically to validate the analytical results and show the band structure for different quasiperiodic patterns, load resistors, and electromechanical coupling coefficients. Furthermore, the mode shapes are presented here for a semi-infinite structure showing localized vibration within the bandgaps. The results demonstrate that quasiperiodic metamaterials with electromechanical local resonators can be used to harvest energy without changing the topology of the bandgaps for the case of weak electromechanical coupling. The observations given here can be used to guide designers in choosing electromechanical resonator parameters and quasiperiodic pattern parameters for an effective energy harvesting metamaterial.