THE FREE-VIBRATIONS OF INHOMOGENEOUS ELASTIC CYLINDERS AND SPHERES

The variational statement, governing equations and corresponding Ritz approximations are derived in Cartesian, cylindrical and spherical coordinates for the evaluation of the natural frequencies of free vibrations of elastic cylinders and spheres. The formulation can account for orthotropic material symmetry, and can be applied to either solid or hollow geometries. The approximating functions selected for the displacement components depend on the geometry and coordinate system used to describe the problem, and are a combination of power series, Fourier series and spherical harmonics. Representative examples are given in the various coordinate systems for both the cylinder and the sphere. In general, excellent agreement is found with results obtained by other methods.