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Self and cross-mode interactions in a weakly nonlinear two-dimensional structural-acoustic waveguide

Bharat, B and Sonti, VR (2020) Self and cross-mode interactions in a weakly nonlinear two-dimensional structural-acoustic waveguide. In: Journal of the Acoustical Society of America, 147 (4). pp. 2499-2510.

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Official URL: https://doi.org/10.1121/10.0001079


In this study, that is entirely semi-analytical, weakly nonlinear wave propagation in an infinite two-dimensional structural-acoustic waveguide is studied. The lower boundary of the waveguide is a rigid wall, while the top boundary is a flexible plate. Both in-plane and transverse displacements are included in the flexible plate model. The acoustic fluid and the plate are modeled using standard nonlinear equations. The waveguide is driven by an oscillating piston at the origin. The regular perturbation method is used to separate the equations at linear and nonlinear order. The self- and cross-mode interactions of the non-orthogonal propagating modes are solved for. It is found that in the self-mode interactions, resonances occur both in pressure and in the in-plane plate displacement at their own different frequencies. Whereas in the cross-mode interactions, there is no in-plane plate resonance and mostly beats (in space) occur except at some frequencies where resonance in pressure is seen. Also, boundary flexibility reduces the number of resonances drastically in comparison to the rigid waveguide. The relevant conditions and closed form solutions are derived for the resonance cases. It is also observed among the nonresonant solutions (or beats) that below the coincidence frequency, the bending mode dominates, and above the coincidence frequency, the acoustic mode dominates

Item Type: Journal Article
Publication: Journal of the Acoustical Society of America
Publisher: Acoustical Society of America
Additional Information: The copyright for this article belongs to the Acoustical Society of America
Keywords: Acoustic wave propagation; Architectural acoustics; Perturbation techniques; Plates (structural components); Resonance; Waveguides, Closed form solutions; Different frequency; Mode interactions; Plate resonances; Regular perturbations; Structural acoustic waveguides; Transverse displacements; Weakly non-linear, Nonlinear equations, article
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 01 Feb 2023 06:24
Last Modified: 01 Feb 2023 06:24
URI: https://eprints.iisc.ac.in/id/eprint/79666

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