Abstract
Only the case in which the parameter ɛ=ka≪1 is considered in this paper, where k is the wave number and a is the characteristic radius of the cross-section of the hole. The general asymptotic expansion of the complex velocity potential of a long wave propagating in the hole with variable cross-section is obtained by regular perturbation: The methods of matched asymptotic expansion are employed to calculate the reflection coefficients, scattering coefficients and radiation coefficients at the open ends of the hole when a long wave propagates through it, which may be open at both ends or only at one end. Three examples of different kinds of holes are given to show the way to solve such two-dimensional or three-dimensional problems.
Similar content being viewed by others
References
Gu Sheng-shi and Fang Kuang-xiong,Propagation of a long wave in a curved duct (I) Basic analysis of long wave propagation in a curved duct with variable cross-section, Applied Mathematics and Mechanics, Vol. 4, No. 1, Feb., (1983).
Lu Ting and J. B. Keller,Radiation from the open end of a cylindrical or conical pipe and scattering from the end of a rod or slab, J. Acoust. Soc. Am. Vol. 61, No. 6, June (1977).
Lesser, M. B. and J. A. Lewis,Applications of matched expansion methods to acoustics I & II, J. Acoust. Soc. AM; 51, (1972); 1664–1669, Am. 52, (1972) 1406–1410.
Author information
Authors and Affiliations
Additional information
Communicated by Duan Zhu-ping.
Rights and permissions
About this article
Cite this article
Kuang-xiong, F., Sheng-shi, G. Propagation of a long wave in a curved duct (II) applications of matched expansion to long wave propagation through a hole with variable cross-section. Appl Math Mech 4, 205–220 (1983). https://doi.org/10.1007/BF01895445
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01895445