On the Forced Torsional Vibrations of an Encased Hollow Cylinder of Finite Length

摘要

A hollow isotropic elastic cylinder of finite length is encased in a thin isotropic elastic shell. The lower end-section of the cylinder is fixed, and a time dependent displacement is prescribed at the upper end section. The inner and outer curved surfaces of the system are traction free, but the displacement and the stresses are assumed to be continuous at the interface between the core and the casing. In order to satisfy the differential equation and the boundary conditions, which include derivatives of the dependent variable with respect to time, associated with the forced torsional motion of the system, a modified Fourier-Bessel analysis is employed. The resulting representation of the circumferential displacement may be differentiated term by term to yield expressions for the shear stresses. (Author)