Numerical Analysis of Chaos in a Phononic Crystal Waveguide with Circular Inclusions of Real Materials

Abstract

Phononic crystal waveguides (PnCW) have been of great interest due to their properties of manipulating or filtering the acoustic waves with which they interact. Similarly, the presence of the phenomenon of chaos in the classical transport of particles through billiards with analogous geometries has been investigated. With this in consideration, in the present work an acoustic system of a two-dimensional PnCW is modeled, composed of two plane-parallel plates and a periodic arrangement of circular cylindrical inclusions with acoustic surfaces of real materials. In this system, we use the numerical technique of the integral equation, which allows us to obtain the pressure field corresponding to the normal modes in a range of frequencies. In addition, spatial statistical properties of pressure intensity such as the autocorrelation function (ACF) and its standard deviation called correlation length were calculated. The results show that when the correlation length is very small, the system presents disordered patterns of field intensities. Thus under certain conditions, the system under consideration presents a chaotic behavior, similar to the corresponding classical system.