Vibration studies of rotating cylindrical shells with arbitrary edges using characteristic orthogonal polynomials in the Rayleigh–Ritz method

A general approach is presented for the vibration studies of rotating cylindrical shells having arbitrary edges. The present analysis is based on the Sandersʹ shell theory and the effects of centrifugal and Coriolis forces as well as initial hoop tension due to rotating are all taken into account. By taking the characteristic orthogonal polynomial series as the admissible functions, the Rayleigh–Ritz method is employed to derive the frequency equations of rotating cylinders with classical homogeneous boundary conditions. Further, utilizing artificial springs to simulate the elastic constraints imposed on the cylinders’ edges, one can derive the frequency equations of rotating cylindrical shells with more general boundary conditions by considering the strain energy of artificial springs during the Rayleigh–Ritz procedure. To validate the approach proposed in this paper, a series of comparison and convergence studies are performed and the investigations demonstrate high accuracy and low computational cost of the present approach. Finally, some further numerical results are given to illustrate the influence of the variations of spring stiffness on the frequencies of rotating cylinders.