The propagation of small amplitude nonlinear waves in a strongly inhomogeneous medium

Abstract

A small amplitude wave is propagated into a semi-infinite, strongly inhomogeneous, nonlinear elastic material. The inhomogeneity is chosen, as in functionally graded materials, so that a closed form exact solution is possible within linear theory. The relationship with the approximate solution described by geometrical acoustics, when the inhomogeneity is slowly varying, is readily seen. The nonlinear result is derived by adjusting the linear characteristic as in Whitham’s nonlinearization technique. Shocks may then occur.

Keywords

strong inhomogeneity functionally graded material geometrical acoustics nonlinear wave shocks

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