Three-dimensional free vibration analysis of inhomogeneous thick orthotropic shells of revolution using differential quadrature

A procedure is developed to determine the natural frequencies of vibration of thick orthotropic shells of revolution consisting of a material having a radial variation of properties. Governing equations are developed using the linear orthotropic three-dimensional theory of elasticity, and a numerical solution is obtained using the differential quadrature method. The solution has geometric generality in that thick shells of revolution with arbitrary constant thickness and smoothly varying meridian can be considered. The method is validated through comparisons with previously published results, including results for a thick transversely isotropic spherical shell with radially varying material properties. Sample results are given for a thick inhomogeneous toroidal shell, and conclusions are drawn.