Reflection and Transmission of Circularly Polarized Elastic Waves of Finite Amplitude

[+] Author and Article Information
M. M. Carroll

Department of Mechanical Engineering, University of California, Berkeley, Calif. 94720

J. Appl. Mech 46(4), 867-872 (Dec 01, 1979) (6 pages) doi:10.1115/1.3424669 History: Received March 01, 1979; Revised June 01, 1979; Online July 12, 2010


Finite amplitude standing wave solutions, obtained previously, are specialized to the case of incompressible isotropic elastic solids with cubic or quintic shear response. This allows closed-form expressions for the motion and stress field, in terms of Jacobian elliptic functions and elliptic integrals and furnishes solutions for approximate finite elasticity theories in which terms up to sixth degree in the stress and strains are retained. The solutions for reflection from free or fixed boundaries, for resonant standing waves in a plate, and for reflection and transmission at a plane boundary are examined in the context of the third and fourth-order approximations.

Copyright © 1979 by ASME
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