Determination of Transient Responses of a Thick-Walled Spherical Shell by the Ray Theory

[+] Author and Article Information
Yih-Hsing Pao, Ahmet N. Ceranoglu

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N. Y.

J. Appl. Mech 45(1), 114-122 (Mar 01, 1978) (9 pages) doi:10.1115/1.3424212 History: Received October 01, 1976; Revised September 01, 1977; Online July 12, 2010


The dynamic response of a thick-walled elastic spherical shell subject to radially symmetric loadings is studied by applying the theory of rays. The Fourier transformed solution of the waves in the shell is sorted out into rays by following the ray-path of the multiply reflected waves at both surfaces. Inverse transform of each ray, which is obtainable in closed form, gives rise to the exact solution of the transient response up to the arrival time of the next ray. Numerical results are shown for internally applied pressure with a step or a square-time function. The radial stresses are found to be critically large in tension due to multiple reflections at both surfaces of a thick shell.

Copyright © 1978 by ASME
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