Precise and target-oriented control of the low-frequency Lamb wave bandgaps

Abstract

Precise and target-oriented control of acoustic/elastic wave bandgaps in phononic crystals or acoustic metamaterials according to particular requirements is of both theoretical and practical importance. A very challenging and also interesting task is to tune the widths and the overall positions of the bandgaps of interest independently and arbitrarily. This work presents a simple and smart acoustic metamaterial structure, which can achieve the above mentioned goal by considering the symmetric Lamb waves. The proposed acoustic metamaterial structure consists of a homogenous piezoelectric plate which is connected to the LC circuits through an array of periodic surface electrodes. The control of the resonance bandgaps (RBGs), which are generated by the coupled resonance of the piezoelectric plate with the external LC circuits, is the focus of this study. To solve the problem at hand, we develop a two-dimensional (2D) spectral element method (SEM) considering the full electro-mechanical coupling, and the high tunability of the RBGs is demonstrated numerically in the low-frequency range. Especially, we find that the upper/lower boundary of a RGB can be intentionally fixed at any specified frequency while changing its’ bandwidth. To explore the corresponding physical phenomena and reveal the regulation mechanism, a simplified theory is developed based on the assumption of thin piezoelectric plates. Several simple analytical formulas are established, which are essential to the precise control of the RBGs for both the thin and thick piezoelectric plates. A numerical example is given to demonstrate the detailed procedure of precisely tuning a RBG in a targeted frequency range, which is also verified by the transmission spectrum for the corresponding finite piezoelectric acoustic metamaterial plate.