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research-article

SEPARATION OF TRAVELING AND STANDING WAVES IN A RIGID-WALLED CIRCULAR DUCT CONTAINING AN INTERMEDIATE IMPEDANCE DISCONTINUITY

[+] Author and Article Information
Yongxiong Xiao

College of Mechanical Engineering Key Laboratory for Special Purpose Equipment and Advanced Manufacturing Technology Ministry of Education and Zhejiang Province Zhejiang University of Technology 18 Chaowang Road Hangzhou 310014, China
ethanxiao_svlab@163.com

Antoine Blanchard

Department of Aerospace Engineering University of Illinois at Urbana-Champaign 104 South Wright Street Urbana, IL 61801, USA
ablancha@illinois.edu

Yao Zhang

College of Mechanical Engineering Key Laboratory for Special Purpose Equipment and Advanced Manufacturing Technology Ministry of Education and Zhejiang Province Zhejiang University of Technology 18 Chaowang Road Hangzhou 310014, China
zhangyao_svlab@163.com

Huancai Lu

College of Mechanical Engineering Key Laboratory for Signal Processing of Zhejiang Province Zhejiang University of Technology 18 Chaowang Road Hangzhou 310014, China
huancailu@zjut.edu.cn

Michael McFarland

Department of Aerospace Engineering University of Illinois at Urbana-Champaign 104 South Wright Street Urbana, IL 61801, USA
dmmcf@illinois.edu

Alexander F. Vakakis

Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign 1208 West Green Street Urbana, IL 61801, USA
avakakis@illinois.edu

Lawrence A. Bergman

Department of Aerospace Engineering University of Illinois at Urbana-Champaign 104 South Wright Street Urbana, IL 61801, USA
lbergman@illinois.edu

1Corresponding author.

ASME doi:10.1115/1.4036866 History: Received August 21, 2016; Revised April 07, 2017

Abstract

In this paper, we study the phenomenon of separation of traveling and standing waves in a one-dimensional rigid-walled circular duct. The underlying mechanism for separation, mode complexity, is linear and introduced here by a damped side branch representing an impedance discontinuity. The left end of the duct is driven at a single frequency by a harmonic acoustic source, and the right end is a rigid termination. The position and impedance of the side branch are independent parameters in the analysis. Sufficient conditions for acoustic wave separation in the duct are derived analytically and employed in a three-dimensional finite element analysis to verify the theoretical result. A physical experiment, consisting of a circular duct with a damped side branch, was constructed based on analytical predictions, the physical parameters were measured or identified, and its performance was documented. These experimental parameters were employed in a second three-dimensional finite element analysis to obtain a direct comparison with experimental results. The comparison reveals the extent to which higher-order (unmodeled) effects degrade the separation phenomenon. It is demonstrated that an intermediate damped side branch used as a non-resonant device can be predictively designed to achieve nearly ideal separation of traveling and standing waves in a rigid-walled circular duct in order to direct and control acoustic energy transmission through the duct system.

Copyright (c) 2017 by ASME
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