We have previously shown how Thévenin's theorem may be used to solve problems in linear acoustic scattering from a mobile body, by forming the solution as a superposition of the field scattered from the body when held immobile and the solution for radiation from the body in a quiescent field (Williams, R. P. and Hall, N. A., 2016, “Thévenin Acoustics” J. Acoust. Soc. Am., 140(6), pp. 4449–4455). For problems involving scattering from multiple mobile bodies, the approach can be extended by using multiport network formalism. The use of network formalism allows for the effects of multiple scattering to be treated using analogous circuit models, facilitating the integration of scattering effects into circuit-based models of acoustic transducers. In this paper, we first review Thévenin's theorem for electrical and linear acoustic systems, and discuss the Thévenin-inspired approach to scattering from one rigid, mobile cylinder. Two-port formalism is introduced as a way to address problems involving two scatterers. The method is illustrated using the problem of scattering from a pair of rigid, mobile cylinders in an ideal plane progressive wave. The velocities of the cylinders and the resultant pressure field in response to the incoming wave are found. Unique features of the method compared to more conventional approaches are discussed.
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February 2019
Research-Article
A Thévenin-Inspired Approach to Multiple Scattering in Acoustics
Randall P. Williams,
Randall P. Williams
Department of Electrical and
Computer Engineering,
The University of Texas at Austin,
10100 Burnet Rd., Bldg. 160,
Austin, TX 78758
e-mail: randy.williams@utexas.edu
Computer Engineering,
The University of Texas at Austin,
10100 Burnet Rd., Bldg. 160,
Austin, TX 78758
e-mail: randy.williams@utexas.edu
Search for other works by this author on:
Neal A. Hall
Neal A. Hall
Department of Electrical and
Computer Engineering,
The University of Texas at Austin,
10100 Burnet Rd., Bldg. 160,
Austin, TX 78758
e-mail: nahall@mail.utexas.edu
Computer Engineering,
The University of Texas at Austin,
10100 Burnet Rd., Bldg. 160,
Austin, TX 78758
e-mail: nahall@mail.utexas.edu
Search for other works by this author on:
Randall P. Williams
Department of Electrical and
Computer Engineering,
The University of Texas at Austin,
10100 Burnet Rd., Bldg. 160,
Austin, TX 78758
e-mail: randy.williams@utexas.edu
Computer Engineering,
The University of Texas at Austin,
10100 Burnet Rd., Bldg. 160,
Austin, TX 78758
e-mail: randy.williams@utexas.edu
Neal A. Hall
Department of Electrical and
Computer Engineering,
The University of Texas at Austin,
10100 Burnet Rd., Bldg. 160,
Austin, TX 78758
e-mail: nahall@mail.utexas.edu
Computer Engineering,
The University of Texas at Austin,
10100 Burnet Rd., Bldg. 160,
Austin, TX 78758
e-mail: nahall@mail.utexas.edu
1Corresponding author.
Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 22, 2018; final manuscript received July 10, 2018; published online September 10, 2018. Assoc. Editor: Ronald N. Miles.
J. Vib. Acoust. Feb 2019, 141(1): 011016 (12 pages)
Published Online: September 10, 2018
Article history
Received:
May 22, 2018
Revised:
July 10, 2018
Citation
Williams, R. P., and Hall, N. A. (September 10, 2018). "A Thévenin-Inspired Approach to Multiple Scattering in Acoustics." ASME. J. Vib. Acoust. February 2019; 141(1): 011016. https://doi.org/10.1115/1.4040927
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