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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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