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Vibrations of a rectangular orthotropic plate with free edges: Analysis and solution of an infinite system

  • Classical Problems of Linear Acoustics and Wave Theory
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Abstract

A new asymptotically exact solution is obtained for the problem of transverse vibrations of a rectangular orthotropic plate with free edges. The general solution to the vibration equation is constructed as the sum of Fourier series with unknown coefficients, which are related by a homogeneous quasi-regular infinite system of linear algebraic equations. Analysis of the infinite system makes it possible to determine the power-law asymptotics for a nontrivial solution to the system, which makes it possible to calculate the natural vibration frequencies and to construct the corresponding eigenmodes. Examples of numerical calculations for real materials are presented.

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Authors and Affiliations

  1. Sevastopol National Technical University, ul. Universitetskaya 33, Sevastopol, Russia

    S. O. Papkov

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  1. S. O. Papkov
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Correspondence to S. O. Papkov.

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Original Russian Text © S.O. Papkov, 2015, published in Akusticheskii Zhurnal, 2015, Vol. 61, No. 2, pp. 152–160.

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Papkov, S.O. Vibrations of a rectangular orthotropic plate with free edges: Analysis and solution of an infinite system. Acoust. Phys. 61, 136–143 (2015). https://doi.org/10.1134/S106377101501008X

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  • DOI: https://doi.org/10.1134/S106377101501008X

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