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 nonresonant 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.
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December 2017
Research-Article
Separation of Traveling and Standing Waves in a Rigid-Walled Circular Duct Containing an Intermediate Impedance Discontinuity
Yongxiong Xiao,
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
e-mail: ethanxiao_svlab@163.com
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
e-mail: ethanxiao_svlab@163.com
Search for other works by this author on:
Antoine Blanchard,
Antoine Blanchard
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: ablancha@illinois.edu
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: ablancha@illinois.edu
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Yao Zhang,
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
e-mail: zhangyao_svlab@163.com
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
e-mail: zhangyao_svlab@163.com
Search for other works by this author on:
Huancai Lu,
Huancai Lu
Mem. ASME
College of Mechanical Engineering,
Key Laboratory for Signal Processing
of Zhejiang Province,
Zhejiang University of Technology,
18 Chaowang Road,
Hangzhou 310014, China
e-mail: huancailu@zjut.edu.cn
College of Mechanical Engineering,
Key Laboratory for Signal Processing
of Zhejiang Province,
Zhejiang University of Technology,
18 Chaowang Road,
Hangzhou 310014, China
e-mail: huancailu@zjut.edu.cn
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D. Michael McFarland,
D. Michael McFarland
Mem. ASME
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: dmmcf@illinois.edu
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: dmmcf@illinois.edu
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Alexander F. Vakakis,
Alexander F. Vakakis
Fellow ASME
Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
1208 West Green Street,
Urbana, IL 61801
e-mail: avakakis@illinois.edu
Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
1208 West Green Street,
Urbana, IL 61801
e-mail: avakakis@illinois.edu
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Lawrence A. Bergman
Lawrence A. Bergman
Fellow ASME
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: lbergman@illinois.edu
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: lbergman@illinois.edu
Search for other works by this author on:
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
e-mail: ethanxiao_svlab@163.com
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
e-mail: ethanxiao_svlab@163.com
Antoine Blanchard
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: ablancha@illinois.edu
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: 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
e-mail: zhangyao_svlab@163.com
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
e-mail: zhangyao_svlab@163.com
Huancai Lu
Mem. ASME
College of Mechanical Engineering,
Key Laboratory for Signal Processing
of Zhejiang Province,
Zhejiang University of Technology,
18 Chaowang Road,
Hangzhou 310014, China
e-mail: huancailu@zjut.edu.cn
College of Mechanical Engineering,
Key Laboratory for Signal Processing
of Zhejiang Province,
Zhejiang University of Technology,
18 Chaowang Road,
Hangzhou 310014, China
e-mail: huancailu@zjut.edu.cn
D. Michael McFarland
Mem. ASME
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: dmmcf@illinois.edu
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: dmmcf@illinois.edu
Alexander F. Vakakis
Fellow ASME
Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
1208 West Green Street,
Urbana, IL 61801
e-mail: avakakis@illinois.edu
Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
1208 West Green Street,
Urbana, IL 61801
e-mail: avakakis@illinois.edu
Lawrence A. Bergman
Fellow ASME
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: lbergman@illinois.edu
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
104 South Wright Street,
Urbana, IL 61801
e-mail: lbergman@illinois.edu
1Corresponding author.
Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 21, 2016; final manuscript received April 7, 2017; published online July 26, 2017. Assoc. Editor: Stefano Lenci.
J. Vib. Acoust. Dec 2017, 139(6): 061001 (8 pages)
Published Online: July 26, 2017
Article history
Received:
August 21, 2016
Revised:
April 7, 2017
Citation
Xiao, Y., Blanchard, A., Zhang, Y., Lu, H., Michael McFarland, D., Vakakis, A. F., and Bergman, L. A. (July 26, 2017). "Separation of Traveling and Standing Waves in a Rigid-Walled Circular Duct Containing an Intermediate Impedance Discontinuity." ASME. J. Vib. Acoust. December 2017; 139(6): 061001. https://doi.org/10.1115/1.4036866
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