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Third Approximation in the Analysis of a Quadratic Nonlinear Hyperelastic Cylindrical Wave

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The perturbation method is applied to solve the problem of the propagation of a plane longitudinal harmonic wave in a hyperelastic material described by the classical Murnaghan model. The exact expression of the second-order solution in terms of Hankel functions of zero and first order and their products is derived. A simplification of the expression is considered

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, Ukraine, 03057

    J. J. Rushchitsky, Ya. V. Simchuk & S. V. Sinchilo

  2. National Technical University “KPI,”, 32 Pobedy Av., Kyiv, Ukraine, 03034

    J. J. Rushchitsky, Ya. V. Simchuk & S. V. Sinchilo

Authors
  1. J. J. Rushchitsky
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  2. Ya. V. Simchuk
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  3. S. V. Sinchilo
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Correspondence to J. J. Rushchitsky.

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Translated from Prikladnaya Mekhanika, Vol. 51, No. 3, pp. 76–85, May–June 2015.

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Rushchitsky, J.J., Simchuk, Y.V. & Sinchilo, S.V. Third Approximation in the Analysis of a Quadratic Nonlinear Hyperelastic Cylindrical Wave. Int Appl Mech 51, 311–318 (2015). https://doi.org/10.1007/s10778-015-0691-9

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  • DOI: https://doi.org/10.1007/s10778-015-0691-9

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