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Two modes nonresonant interaction for rectangular plate with geometrical nonlinearity

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Abstract

The vibrations of thin rectangular plate with geometrical nonlinearity are analyzed. The models of plate vibrations with different numbers of degrees-of-freedom are derived. It is deduced that two degrees-of-freedoms are enough to describe low-frequency nonlinear dynamics of plates. Nonlinear normal modes are used to analyze the system dynamics. If vibrations amplitudes are increased, single-mode plate vibrations are transformed into two mode ones. In this case, internal resonance conditions are not observed. Such transformation of vibration is described using Kauderer–Rosenberg nonlinear normal modes.

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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. Pozharskogo St., 61046, Kharkov, 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. Two modes nonresonant interaction for rectangular plate with geometrical nonlinearity. Nonlinear Dyn 69, 285–294 (2012). https://doi.org/10.1007/s11071-011-0264-3

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  • DOI: https://doi.org/10.1007/s11071-011-0264-3

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