Abstract
Frequency equations and mode displacement functions have been derived for the plane strain, free transverse vibration of a cylindrical assembly consisting of a solid elastic core bonded to a thin elastic shell. Deformation of the elastic core obeys Navier’s equation of elastodynamics while deformation of the casing in extension and in bending occurs in accordance with the equations of thin shell theory. Two different solutions are presented; one is applicable to a compressible and the other to an incompressible core material. It is found that with a compressible core, the rotationally symmetric mode has two uncoupled motions; one is a rigid body rotation of the casing with a twisting of the cylinder and the other is a radial “breathing” of the casing and the cylinder. The breathing mode is not present with an incompressible core. Some simplified frequency equations are also presented for limiting extremes of rigidity and density.
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