A variational method for free vibration analysis of joined cylindrical-conical shells

A variational method is proposed to study the free vibration of joined cylindrical-conical shells (JCCSs) subjected to classical and non-classical boundary conditions. A JCCS is divided into its components (i.e., conical and cylindrical shells) at the cone-cylinder junction. The interface continuity and geometric boundary conditions are approximately enforced by means of a modified variational principle and least-squares weighted residual method. No constraints need to be imposed a priori in the admissible displacement functions for each shell component. Reissner-Naghdi's thin shell theory is used to formulate the theoretical model. Double mixed series, i.e. the Fourier series and Chebyshev orthogonal polynomials, are adopted as admissible displacement functions for each shell component. To test the convergence, efficiency and accuracy of the present method, free vibrations of JCCSs are examined under various combinations of edge support conditions. The results obtained in this study are found to be in a good agreement with previously published results where possible, and those from the finite element program ANSYS. The effects of elastic foundation stiffness and semi-vertex angle on frequency characteristics of the JCCSs are also discussed.