Nonaxisymmetric free vibrations of a spherically isotropic spherical shell embedded in an elastic medium

Based on three-dimensional elastic theory, the nonaxisymmetric free vibrations of a spherically isotropic spherical shell embedded in an elastic medium are studied in the paper. Three displacement functions are introduced to simplify the governing equations of a spherically isotropic medium for free vibrational problem. The Pasternak’s assumption is adopted for the elastic medium, for which the P-i relation in the spherical coordinates is derived by the principle of minimum potential energy. It is found that the vibration of an embedded spherical shell can be divided into two classes, as the case in vacuum. The first class is identical to the corresponding one in vacuum, and the second has changed due to the effect of the surrounding medium. Numerical results are carried out to clarify the effect of relative parameters. Copyright SF;! 1996 Elsevier Science Ltd