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DISPERSION AND SPATIAL LOCALIZATION OF BENDING WAVES PROPAGATING IN A TIMOSHENKO BEAM LAYING ON A NONLINEAR ELASTIC BASE

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Abstract—

In this article, we consider flexural (bending) waves propagating in a homogeneous beam fixed on a nonlinear elastic foundation. The dynamic behavior of the beam is determined by Timoshenko’s theory. The system of equations describing the bending vibrations of the beam is reduced to a single nonlinear fourth-order equation for the transverse displacements of the beam median line particles. We state that if the beam stiffness is small compared to the linear stiffness of the foundation, the evolutionary equation is a modified Ostrovsky equation with an additional third-order nonlinear term. For the evolutionary equation, exact soliton solutions are found from the class of stationary waves in the form of a kink and an antikink.

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Funding

This study was financially supported by the Russian Science Foundation (project no. 20-19-00613).

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Authors and Affiliations

  1. Mechanical Engineering Research Institute, Branch of Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences, 603024, Nizhniy Novgorod, Russia

    V. I. Erofeev & A. V. Leontieva

Authors
  1. V. I. Erofeev
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  2. A. V. Leontieva
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Correspondence to V. I. Erofeev or A. V. Leontieva.

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Translated by A.A. Borimova

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Erofeev, V.I., Leontieva, A.V. DISPERSION AND SPATIAL LOCALIZATION OF BENDING WAVES PROPAGATING IN A TIMOSHENKO BEAM LAYING ON A NONLINEAR ELASTIC BASE. Mech. Solids 56, 443–454 (2021). https://doi.org/10.3103/S0025654421040051

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