ASA 127th Meeting M.I.T. 1994 June 6-10

1aSA13. Asymptotically correct shell theories with fluid loading for the thin spherical shell: New results.

Cleon E. Dean

Dept. of Phys., Georgia Southern Univ., Landrum Box 8031, Statesboro, GA 30460

Michael F. Werby

Code 7181, NRL, Stennis Space Center, MS 39529-5004

In a previous paper [C. E. Dean and M. F. Werby, J. Acoust. Soc. Am. 91, 2440 (A) (1992)] further results in the derivation of a so-called ``shell theory'' incorporating proper high ka asymptotic behavior for the Lamb flexural and extensional modes for a thin spherical shell were given. Shell theories give reasonably good results for the motion of a bounded elastic shell by positing that various parts of the shell move together in some reasonable manner. They also give physical insight into the motions of the shell while using less computational time and resources than exact elastodynamic calculations. The use of various assumptions about the motions and fluid loading of the thin spherical shell gives rise to several shell theories. New results from the derivation of an asymptotically correct shell theory with fluid loading for the thin spherical shell are compared with the exact results from modal analysis with particular emphasis on the large size parameter (large ka) limit for the flexural and extensional Lamb modes. Limitations of each of the methods are then outlined as well as those of shell methods in general. [Initial work in this area supported by ONR/NRL and by ONT Postdoctoral Fellowship Program.]