Resonance and beating phenomenon in a nonlinear rigid cylindrical acoustic waveguide: The axisymmetric mode

Bharat, Biswajit and Sonti, Venkata R (2019) Resonance and beating phenomenon in a nonlinear rigid cylindrical acoustic waveguide: The axisymmetric mode. In: JOURNAL OF SOUND AND VIBRATION, 458 . pp. 262-275.

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Abstract

A rigid-walled semi-infinite circular cylindrical waveguide enclosing a weakly nonlinear fluid is considered. A quadratic nonlinear interaction is assumed as a model. A flat rigid piston generates an axisymmetric harmonic pressure that is prescribed as the input at the finite end of the waveguide. The objective is to study the modal interactions of waves. A regular perturbation method is used to separate the linear (primary) and the quasilinear (second harmonic) equations. First, linear solutions are established. Their quasilinear interactions then lead to modal interactions. Typically, the linear wavenumbers at the quasilinear order generate homogenous wavenumbers. Intersections of both these wavenumbers in the wavenumber-frequency plane are considered as resonances since the resulting pressure grows in amplitude in the axial propagating direction. The conditions under which the solutions become resonant or non-resonant are presented. In this last case, a beating phenomenon occurs with distance. It is found that the resonances are rare, except for the plane wave. Generally, the forced linear wavenumbers and the quasilinear generated wavenumbers acquire numerical values close to each other and create the beating phenomenon. (C) 2019 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	JOURNAL OF SOUND AND VIBRATION
Publisher:	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Additional Information:	Copyright of this article belongs to ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Keywords:	Modal interactions; Resonant interaction; Nonlinear wave propagation; Cylindrical waveguide; Nonlinear acoustics; Beating; Bessel-Fourier
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	13 Nov 2019 05:44
Last Modified:	13 Nov 2019 05:44
URI:	http://eprints.iisc.ac.in/id/eprint/63439

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