Torsional vibration of a coupled cylinder

The torsion loading of a coupled cylinder, comprising distinct upper and lower cylindrical sections potentially made of different materials, is considered. The bottom of the cylinder is fixed in place, and induces the cylinder vibration. The torsion is applied via an arbitrary loading on the upper face. Three forms of coupling condition between the upper and lower cylinders are outlined: ideal, soft (weak), and rigid (hard/ stiff) contact. The resulting displacements and tangential stresses are obtained using the finite Hankel transform, and a Green's function representation of the displacement. Numerical results are provided, and the impact of the differing coupling conditions investigated for a range of cylinder geometries, material properties and vibration rates. The resonance frequencies of the coupled cylinder are determined. A method for using the coupled cylinder model to approximate the displacement of a cylinder containing a damaged region via a weak interfacial layer is outlined. The properties of the weak interface layer needed for this approximation are determined, and the advantages of its use in non-destructive testing are discussed.