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Modified Elliptic Integral Approach for the Forced Vibration and Sound Transmission Analysis of a Nonlinear Panel Backed by a Partitioned Cavity

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  • Yiu-Yin Lee

    (Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon 852, Hong Kong)

Abstract

This article is the further work of previous papers and also the first study to adopt the elliptic integral approach to solve the forced nonlinear structural acoustic problem. A previous elliptic integral approach, which was only used for the free vibration analyses of various nonlinear structural acoustic problems, is modified and custom designed for conducting this forced vibration analysis. The main advantage of the proposed approach is that one elliptic cosine contains various harmonic components, while one simple cosine term only carries one particular harmonic component. That is why the proposed solution form can be more concise than those in the harmonic balance procedures. This is the first study to employ the proposed elliptic cosine solution form for the forced vibration and sound transmission of a nonlinear panel backed by a partitioned cavity. This study has two focuses: (1) the development of elliptic integral approach for solving the nonlinear structural acoustic governing equations, and (2) the effect of partitioned cavities on the forced vibration response and sound transmission loss. Moreover, a set of elliptic cosine solutions is verified by that from the modified residue harmonic balance method. A mode convergence study and a harmonic contribution analysis are also conducted.

Suggested Citation

  • Yiu-Yin Lee, 2022. "Modified Elliptic Integral Approach for the Forced Vibration and Sound Transmission Analysis of a Nonlinear Panel Backed by a Partitioned Cavity," Mathematics, MDPI, vol. 10(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:984-:d:774668
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    References listed on IDEAS

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    1. Yiu-Yin Lee, 2019. "The effect of large amplitude vibration on the pressure-dependent absorption of a structure multiple cavity system," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-27, July.
    2. Yiu-yin Lee, 2020. "Free Vibration Analysis of Nonlinear Structural-Acoustic System with Non-Rigid Boundaries Using the Elliptic Integral Approach," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
    3. Soledad Moreno-Pulido & Francisco Javier García-Pacheco & Alberto Sánchez-Alzola & Alejandro Rincón-Casado, 2021. "Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations," Mathematics, MDPI, vol. 9(9), pages 1-16, May.
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    Cited by:

    1. Geman Shi & Xiaoxun Wu & Renjie Jiang & Shande Li, 2023. "A Particle Reinforced Gradient Honeycomb Sandwich Panel for Broadband Sound Insulation," Mathematics, MDPI, vol. 11(3), pages 1-16, January.

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