Quadratically Nonlinear Cylindrical Hyperelastic Waves: Derivation of Wave Equations for Plane-Strain State |
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Authors: | J. J. Rushchitsky |
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Affiliation: | (1) S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine |
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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__________Translated from Prikladnaya Mekhanika,Vol. 41, No. 5, pp. 40–51, May 2005. |
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Keywords: | nonlinear continuum mechanics rigorous approach nonlinear hyperelastic cylindrical waves quadratically nonlinear wave equations geometrical and physical nonlinearities plane strain state |
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