Abstract
A method based on the Rayleigh-Ritz technique is used to study the natural vibrations of elastic spheres composed of an arbitrary number of spherical layers, each with distinct density and spherically orthotropic (transversely isotropic) properties. The basic form of the displacement field known from studies of isotropic spheres is employed, except for the radial dependence which is taken in an approximate manner by considering the sphere to be an assemblage of a large number of spherical laminas; for each lamina, the radial dependence of the displacement field is characterized by a discrete number of generalized coordinates. The approximation results in two algebraic eigenvalue problems which are solved for examples of isotropic and.laminated orthotropic spheres.
Published Version
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