Structure of the frequency spectrum of nonaxisymmetric vibrations of a transversally isotropic hollow ball

We consider nonaxisymmetric vibrations of a hollow sphere made of a spherically Isotropic material. The original boundary-value problem is reduced to a system of ordinary differential equations by introducing new unknown junctions and expanding the sought solution in a series in spherical functions. The nonaxisymmetric problem of vibrations of a hollow ball decomposes into two independent problems that describe modes of first and second kind. The frequency spectrum for modes of first and second kind is analyzed.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 32–35, 1986.