Abstract
A plane standing wave solution is obtained for homogeneous, isotropic, incompressible nonlinearly elastic solids. The motion describes the nonlinear interaction of two oppositely propagating, circularly polarized waves. It is used to obtain exact steady state solutions for nonlinear vibrations of a plate and for reflection and transmission of finite amplitude, circularly polarized waves at a plane interface.
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Carroll, M. M., Some results on finite amplitude elastic waves, Acta Mech., 3, 1967, pp. 167–181.
John, F., Plane waves of finite amplitude, Studies in Applied Mathematics, 5. Advances in Differential and Integral Equations, SIAM, 1969, pp. 14–19.
Carroll, M. M., On circularly-polarized nonlinear electromagnetic waves, Quart. Appl. Math., 25, 1967, pp. 319–323.
Cekirge, H. M. and Varley, E., Large amplitude waves in bounded media I, Phil. Trans. R. Soc. Lond., A273, 1973, pp. 261–313.
Kazakia, J. I. and Varley, E., Large amplitude waves in bounded media II, Phil. Trans. R. Soc. Lond., A277, 1974, pp. 191–237.
Kazakia, J. I. and Varley, E., Large amplitude waves in bounded media III, Proc. R. Soc. Lond., A277, 1974, 239–250.
Carroll, M. M., Reflection and transmission of circularly polarized waves in nonlinear dielectrics. Submitted for publication.
Carroll, M. M., Oscillatory shearing of nonlinearly elastic solids, ZAMP, 25, 1974, pp. 83–88.
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Carroll, M.M. Plane elastic standing waves of finite amplitude. J Elasticity 7, 411–424 (1977). https://doi.org/10.1007/BF00041731
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DOI: https://doi.org/10.1007/BF00041731