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Longitudinal and torsional shock waves in anisotropic elastic cylinders. (English) Zbl 1430.74067
Summary: Discontinuities in solutions of one-dimensional hyperbolic equation system describing nonlinear longitudinal and torsional waves propagating in elastic rods are studied. The discontinuity amplitude is assumed to be small so that in the equations all nonlinear terms, except for the quadratic ones, are neglected. The shock adiabat form and evolutionary conditions are analyzed depending on the model parameters. The results of this study can be applied not only to waves in rods, but also to shock waves in anisotropic elastic media. shock waves in rods, elasticity, shock adiabat, evolutionary conditions.
74J30 Nonlinear waves in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74B20 Nonlinear elasticity
74M20 Impact in solid mechanics
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