Free vibration analysis of circular cylindrical shell on elastic foundation using the Rayleigh-Ritz method

A general approach is presented for the free vibration analysis of circular cylindrical shell resting on elastic foundation and subjected to classical boundary conditions of any type. The Winkler/Pasternak model is utilized to simulate the elastic foundation imposed on the cylindrical shell, and then it is easily to derive the potential energy of the elastic foundation. Based on the Flügge shell theory, explicit expressions for the mass and stiffness matrices are obtained. By taking the characteristic beam modal functions as the admissible functions, the Rayleigh-Ritz method is employed to derive the frequency equations of circular cylindrical shell with all the classical boundary conditions and resting on elastic foundation. Once the frequency equation has been determined, the frequencies can be calculated numerically. The excellent accuracy and validity of the present approach are demonstrated by numerical examples and comparisons with the results available in the literature. Finally, some further numerical results are given to illustrate the comprehensive effect of geometric properties and foundation coefficients on the frequencies of circular cylindrical shell in contact with elastic foundation.