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Nonlinear modes of cylindrical panels with complex boundaries. R-function method

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Abstract

Nonlinear vibrations of cylindrical panels with complex base are analyzed. The Donnell-Mushtari-Vlasov equations with respect to displacements are used to study vibrations of shallow shell with geometrical nonlinearity. R-function method is applied to satisfy the panel boundary conditions. The Rayleigh-Ritz method is used to obtain the linear vibrations eigenmodes, which contain R-function. The nonlinear vibrations of panel are expanded by using these eigenmodes. The harmonic balance method and nonlinear normal modes are used to study the free nonlinear vibrations.

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Authors and Affiliations

  1. Department of Nonstationary Vibrations, A.N. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, 2/10 Dm. Pozharskoho St., 61046, Kharkiv, Ukraine

    I. D. Breslavsky & K. V. Avramov

Authors
  1. I. D. Breslavsky
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  2. K. V. Avramov
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Correspondence to K. V. Avramov.

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Breslavsky, I.D., Avramov, K.V. Nonlinear modes of cylindrical panels with complex boundaries. R-function method. Meccanica 46, 817–832 (2011). https://doi.org/10.1007/s11012-010-9340-x

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  • DOI: https://doi.org/10.1007/s11012-010-9340-x

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