Abstract
The propagation of two-dimensional waves in cylindrical and spherical, homogeneous, elastic layers is investigated. For these layers finite formulas are found for the characteristic matrices. Comparison of these matrices and use of asymptotic representations for the Hankel functions make it possible to derive expressions in the case of weakly curved elastic layers. The expressions obtained correspond to analogous formulas in the form of matrix series.
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Literature cited
L. A. Molotkov, “On characteristic matrices of weakly curved elastic layers,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,99, 74–84 (1980).
L. A. Molotkov, “On interference waves in a free, inhomogeneous, elastic layer,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,34, 117–141 (1973).
L. A. Molotkov, “On low-frequency waves in inhomogeneous, elastic, cylindrical and spherical layers surrounded by a medium,” Vopr. Dinam. Teor. Raspr. Seism. Voln., No. 13, 15–39 (1973).
G. N. Watson, Theory of Bessel Functions, Cambridge Univ. Press.
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 156–169, 1981.
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Molotkov, L.A. Finite expressions for the characteristic matrices of weakly curved elastic layers. J Math Sci 20, 1845–1854 (1982). https://doi.org/10.1007/BF01119369
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DOI: https://doi.org/10.1007/BF01119369