Abstract
A method is proposed for deriving nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical waves. The method is based on a rigorous approach of nonlinear continuum mechanics. Nonlinearity is introduced by means of metric coefficients, Cauchy-Green strain tensor, and Murnaghan potential and corresponds to the quadratic nonlinearity of all basic relationships. For a configuration (state) dependent on the radial and angle coordinates and independent of the axial coordinate, quadratically nonlinear wave equations for stresses are derived and stress-strain relationships are established. Four ways of introducing physical and geometrical nonlinearities to the wave equations are analyzed. For one of the ways, the nonlinear wave equations are written explicitly
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Translated from Prikladnaya Mekhanika,Vol. 41, No. 5, pp. 40–51, May 2005.
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Rushchitsky, J.J. Quadratically Nonlinear Cylindrical Hyperelastic Waves: Derivation of Wave Equations for Plane-Strain State. Int Appl Mech 41, 496–505 (2005). https://doi.org/10.1007/s10778-005-0115-3
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DOI: https://doi.org/10.1007/s10778-005-0115-3