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.

Keywords

• Phononic Crystak Waveguide
• Acoustic chaos
• Integral Equation Method
• Autocorrelation function

Supporting Institution

Coordinación de la investigación cientifíca

Project Number

DESARROLLO DE LOS MODELOS NUMÉRICOS PARA EL ESTUDIO DE GUÍAS DE ONDAS DE CRISTALES FOTÓNICOS Y FONÓNICOS

Ethical Statement

This manuscript has not been published and is not under consideration for publication elsewhere. We have no conflicts of interest to disclose.

Thanks

H. Pérez-Aguilar express their gratitude to the Coordinación de la Investigación Científica of the Universidad Michoacana de San Nicolás de Hidalgo for the financial support granted for the development of this research project. Likewise, this work was supported by Tecnológico Nacional de México (TecNM) unit Morelia, and Consejo Nacional de Humanidades Ciencias y Tecnologías (CONAHCYT).

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