Propagation of Transverse Wave for the Piezoelectric Radial Phononic Crystal Annular Plate in a Fibonacci Order

Based on the previous conventional phononic crystal (PC) structures infinitely periodic in Cartesian coordinates, this paper addresses a new radial phononic crystal annular plate (RPCAP) modeled in a Fibonacci order along the radial direction. In this study, piezoelectric material PZT4 is simultaneously inserted into this RPCAP model to investigate the stop band behaviors. In order to clearly show the transmission characteristics of transverse wave, in cylindrical coordinates, the transfer matrix is deduced through combining the general solutions, piezoelectric governing equations, and continuity conditions. Compared with conventional PC structures, transmission response of transverse vibration for the Fibonacci RPCAP model is calculated theoretically to analyze the stop band phenomenon. Finite element simulation method (FEM) is conducted here to verify the theoretical results. The results show that the Fibonacci RPCAP model presents two newly emerging resonance frequencies while the radial periodic order is disorganized. To thoroughly understand the RPCAP, the effects of structural parameters, material parameters, and piezoelectric parameters on the stop band are discussed in detail. The proposed Fibonacci RPCAP can be employed in many engineering applications, such as in rotating parts which are often coupled with transverse vibration (like gear driving systems).