Characteristic Forms of Differential Equations for Wave Propagation in Nonlinear Media

[+] Author and Article Information
T. C. T. Ting

Department of Materials Engineering, University of Illinois at Chicago Circle, Chicago, Ill. 60680

J. Appl. Mech 48(4), 743-748 (Dec 01, 1981) (6 pages) doi:10.1115/1.3157726 History: Received April 01, 1981; Online July 21, 2009


Characteristic forms of differential equations for wave propagation in nonlinear media are derived directly from equations of motion and equations which combine the constitutive equations and the equations of continuity. Both Lagrangian coordinates and Eulerian coordinates are considered. The constitutive equations considered here apply to a large class of nonlinear materials. The characteristic forms derived here clearly show which components of the stress and velocity are involved in the differentiation along the bicharacteristics. Moreover, the reduction to one-dimensional cases from three-dimensional problems is obvious for the characteristic forms obtained here. Examples are given and compared with the known solution in the literature for wave propagation in linear isotropic elastic solids and isentropic compressible fluids.

Copyright © 1981 by ASME
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