3-DIMENSIONAL AXISYMMETRICAL VIBRATIONS OF ORTHOTROPIC AND CROSS-PLY LAMINATED HOLLOW CYLINDERS

This paper deals with the problem of longitudinal vibrations of homogeneous orthotropic and cross-ply laminated hollow cylinders. The solution of the problem is achieved using a method of successive approximations. The approach is based on the replacement of the hollow cylinder considered with N thin, successive, and coaxial subcylinders. The exact governing equations of each one of these latter fictitious cylinders are replaced by a set of simpler approximate equations that are solved exactly. Connecting all exact solutions obtained by means of appropriate continuity conditions, the corresponding solution of the exact governing equations is successively approached by increasing the value of N. Detailed numerical results dealing with the natural frequencies and vibration mode shapes of homogeneous orthotropic as well as certain two-layered cross-ply cylinders are presented and discussed.