Abstract
The second chapter deals with a three-dimensional dynamic problem of elasticity theory for a spherical layer. In the case of axisymmetric vibrations homogeneous solutions are constructed. One way for the construction of heterogeneous solutions is pointed out. An asymptotic analysis of homogeneous solutions for a spherical shell corresponding to different groups of roots of the dispersion equation is carried out. Non-axisymmetric dynamic problem of elasticity theory for a spherical layer is considered. Due to spherical symmetry, the general boundary value problem is divided into two problems: one coincides with the boundary value problem for axisymmetric vibrations of a hollow sphere, and the second describes the vortex motion of a hollow sphere and coincides with the boundary value problem for purely torsional vibrations of a hollow sphere.
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