Sound Propagation in a Duct with Wall Corrugations Having Square-Wave Profiles

Muhammad A Hawwa

doi:10.1155/2015/516982

Abstract

Acoustic wave propagation in ducts with rigid walls having square-wave wall corrugations is considered in the context of a perturbation formulation. Using the ratio of wall corrugation amplitude to the mean duct half width, a small parameter is defined and a two levels of approximations are obtained. The first-order solution produces an analytical description of the pressure field inside the duct. The second-order solution yields an analytical estimate of the phase speed of waves transmitting through the duct. The effect of wall corrugation density on acoustic impedance and wave speeds is highlighted. The analysis reveals that waves propagating in a duct with square-wave wall corrugation are slower than waves propagating in a duct with sinusoidal wave corrugation having the same corrugation wavelength.

Highlights

Acoustic waveguides with walls having weak periodic undulations have been modules of interest over the past decades
Nayfeh [3] employed a multiple scales perturbation technique to show that the perturbation expansion employed by Samuels [1] and Salant [2] was not uniform under resonance conditions and provided a uniformly valid perturbation expansion
Asfar and Nayfeh [6] provided a review on using the perturbation method of multiple scales for wave propagation in periodic structures, including closedand open-acoustic waveguides

Summary

Introduction

Acoustic waveguides with walls having weak periodic undulations have been modules of interest over the past decades. Hawwa [9] presented a multiple scales perturbation approach for analyzing waveguides with surfaces having two periodicities and detailed scenarios of various incidents and reflected mode coupling in these. Hawwa [11] investigated the effect of chirped periodic surface undulations on widening stopbands of acoustic wave reflection spectra in ducts by solving coupled mode equations describing modal interactions. Tao et al [12] made a predictive study of non-Bragg resonance, caused by the interaction between the transverse standing acoustic waves occurring in a cylindrical waveguide with a sinusoidally perturbed wall. Tao and Fan [17] used a perturbation method and a finite element formulation to consider transmission under non-Bragg resonances of three transverse modes in a waveguide with sinusoidally perturbed walls. The influence of wall corrugation density is considered as a differentiating factor for graphical presentation of obtained analytical results

Mathematical Model and Solution

Discussion and Illustrations

Conclusion