The propagation of small amplitude nonlinear waves in a strongly inhomogeneous medium. (English) Zbl 1269.74132
Summary: 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; shocksReferences:
| [1] | Keller, JB, J Opt Soc Amer 52 pp 116– (1962) · doi:10.1364/JOSA.52.000116 |
| [2] | Lewis, RM The progressing wave formalism. In: Proceedings of the Symposium on Quasi-Optics, Polytechnic Institute of Brooklyn, 1964, pp. 71-103. |
| [3] | Whitham, GB, Linear and Nonlinear Waves (1974) |
| [4] | Seymour, BR, Mechanics Today 2 pp 251– (1975) · doi:10.1016/B978-0-08-018113-4.50010-0 |
| [5] | Collet, B., Eur J Mech, A: Solid 25 pp 695– (2006) · Zbl 1101.74037 · doi:10.1016/j.euromechsol.2006.01.007 |
| [6] | Varley, E., Stud Appl Math 78 pp 183– (1988) · Zbl 0681.35003 · doi:10.1002/sapm1988783183 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
