Acoustic Waves in Phononic Crystal Plates

Abstract

Recently, the study on elastic waves in phononic crystal plates is becoming a research hotspot due to its potential applications, especially in wireless communication, transducer and sensor system [1-10]. The phononic crystal plates commonly consist of two materials with large contrast in elastic properties and densities, arranging in a periodic (or quasiperiodic) array. The absolute band gaps in composite plates can forbid the propagation of all elastic wave modes in all directions. Comparing with the bulk wave and surface acoustic wave devices, phononic crystal plates have better performance in elastic wave propagation since the phase speed of most Lamb wave modes (except for A0 mode) is faster than surface wave mode, and also the wave energy in plates is totally confined between the upper and nether free-stress boundaries regardless of the air damp and self-dissipation, which provides a special potentiality in micro-electronics in wireless communication. The propagation of Lamb waves is much more complicated than bulk wave and surface acoustic wave in terms of the free-stress boundaries which can couple the longitudinal and transversal strain components. The first attempt to describe the propagation of Lamb waves with wavelength comparable with the lattice is due to Auld and co-workers [11-12], who studied 2D composites within the couple-mode approximation. Alippi et al. [13] have presented an experimental study on the stopband phenomenon of lowest-order Lamb waves in piezoelectric periodic composite plates and interpreted their results in terms of a theoretical model, which provides approximate dispersion curves of the lowest Lamb waves in the frequency range below the first thickness mode by assuming no coupling between different Lamb modes. The transmissivity of the finite structure to Lamb wave modes was also calculated by taking into account the effective plate velocities of the two constituent materials [14]. Based on a rigorous theory of elastic wave, Chen et al.[1] have employed plane wave expansion (PWE) method and transient response analysis (TRA) to demonstrate the existence of stop bands for lower-order Lamb wave modes in 1D plate. Gao et al.[8] have developed a virtual plane wave expansion (V-PWE) method to study the substrate effect on the band gaps of lower-order Lamb waves propagating in thin plate with 1D phononic crystal coated on uniform substrate. They also studied the quasiperiodic (Fibonacci system) 1D system and find out the existence of split in phonon band gap [2]. In order to reduce the computational complexity without losing the accuracy, Zhu et al.[9] have promoted an efficient method named harmony response analysis (HRA) and supercell plane wave expansion (SC PWE) to study the behavior of Lamb wave in silicon-based 1D composite plates. Zou et al.[10] have employed V-PWE method to study the band gaps of plate-mode waves in 1D piezoelectric composite plates with substrates.