Three-dimensional free vibration analysis of thick cylindrical shells resting on two-parameter elastic supports

Three-dimensional free vibration of a circular cylindrical shell in contact with an elastic medium will be studied. The response of the elastic medium is formulated by the Winkler/Pasternak model. The layerwise theory, in conjunction with a three-dimensional form of Hamiltonʹs principle, is used to obtain the transversely discretized equations of motion, and the related boundary conditions. The differential quadrature method is employed to discretize the resulting equations in the axial direction and for the solution procedure. To validate the formulation, the results are compared with the available exact solutions and also with ANSYS finite elements solutions. By examining the results for thick circular shells under various boundary conditions and on different elastic foundations, the influence of such parameters, and in particular, those due to elastic foundations are studied.