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Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Prakash, Vijay S and Sonti, Venkata R (2015) Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide. In: JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 138 (5). pp. 3231-3244.

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Official URL: http://dx.doi.org/10.1121/1.4935132

Abstract

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ACOUSTICAL SOC AMER AMER INST PHYSICS, STE 1 NO 1, 2 HUNTINGTON QUADRANGLE, MELVILLE, NY 11747-4502 USA
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Depositing User: Id for Latest eprints
Date Deposited: 14 Jan 2016 06:37
Last Modified: 14 Jan 2016 06:37
URI: http://eprints.iisc.ac.in/id/eprint/53097

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