Exact shell theory analysis of free vibrations of submerged thin spherical shells

By the introduction of two displacement functions, the non-axisymmetric free vibrations of a complete thin isotropic spherical shell submerged in a compressible fluid medium are successfully investigated. It is found that there exist two classes of free vibrations : the first class is not affected by the ambient fluid while the second is. It is further proved that the frequency equations can be expressed in terms of polynomial. For the second class, it is also demonstrated that only complex frequencies exist except for the case of n = 1, for which the trivial solution f~ = 0 emerges. For n = 0, 1 and 2, the frequency equations of the second class are investigated numerically and the effects of various relative parameters are discussed. The small damping coefficient method is also discussed finally in the paper. ʹ,(2) 1998 Elsevier Science Ltd. All rights reserved.