Free vibration analysis of an eccentric hollow cylinder using exact 3D elasticity theory

The translational addition theorem for cylindrical wave functions in conjunction with the appropriate orthogonal series expansions and the pertinent boundary conditions are employed to develop an exact 3D elasticity solution for free vibrations of a simply (shear diaphragm) supported elastic circular cylinder of finite length with an eccentrically located inner circular cavity. The frequency spectrum plots of the first several eigenfrequencies are presented in a wide range of dimensionless eccentricities for selected length-to-radius and inner–outer radius ratios. Also, a detailed study on the 2D free vibration characteristics of an infinite eccentric cylinder is included. The numerical results describe the imperative influence of cavity eccentricity, mode type, and radii and length ratios on the vibrational characteristics of the hollow cylinder. It is observed that the introduction of bore eccentricity causes not only an increase in the number of resonant frequencies through the splitting of degenerate modes of the unperturbed problem, but also changes the appearance order of natural vibration modes. The accuracy of solutions is checked through appropriate convergence studies, and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature.