Study of full band gaps and propagation of acoustic waves in two-dimensional piezoelectric phononic plates

Abstract

Acoustic wave propagation in periodic structures composed of multi-constituents, namely the phononic crystals (PCs), has received much attention in the past decade. Recently, PCs constructed in the form of plate structures with two-dimensional lattices have been investigated, and some important phenomena, such as the full band-gap and waveguiding effects, induced by the periodicities of the phononic plates were reported. One of the virtues using Lamb waves is to perfectly confine the acoustic energy within the plate thickness and guided in structures with only 2D lattices rather than 3D lattices; however, the additional free surfaces derive much more complicated characteristics which are still awaiting study further. In this study, we investigate the band-gap and propagation properties of waves in two-dimensional phononic plates that consist of either elastic or piezoelectric materials by employing a revised full 3D plane wave expansion (PWE) method and so on. To apply the PWE method efficiently, Fourier expansions are performed in the thickness direction for an imaginary 3D periodic structure by stacking the phononic plates and vacuum layers alternatively. Moreover, effects of piezoelectricity, lattices, and filling ratios on band gaps are discussed.