Free Vibrations of a Spherically Isotropic Hollow Sphere

In this paper an exact analysis of the nonaxisymmetric vibrations of an aeolotropic hollow sphere is presented. It is found that, as in the case of an isotropic sphere, there are two independent classes of vibrations, viz., the first and second class. In the radial coordinate, the solution for the vibration of the first class is given in terms of Bessel functions, while the solution for the vibration of the second class is obtained using a Frobenius power series. Numerical results are presented giving the lower mode frequencies for different values of sphere thickness to radius ratio, for a variety of spherically isotropic materials. These results are compared with corresponding results predicted on the basis of a shell theory.