Yegao Qu

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-Naghdis 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.

Free vibration of laminated orthotropic conical shell on Pasternak foundation by a domain decomposition method

By a domain decomposition method, free vibration characteristics of laminated orthotropic conical shells resting on Pasternak foundations are analyzed. The conical shell is divided into some conical shell segments in the meridional direction and separated from the geometric boundary and Pasternak foundation; the theoretical model is formulated based on a modified variational functional which includes energy of each conical shell segment, interface potentials (including the boundary potentials) and the energy due to the Pasternak foundation. Numerical comparisons with those published results are made to validate the high accuracy of the present method. The variation of the energy contribution of the shell with different thickness-to-radius ratio, cone angle and fibre orientation against various circumferential wave numbers are presented to help better understand the vibrational characteristics. Moreover, the effects of elastic foundation, boundary condition, stacking sequence and the variations in physical parameters of the shells on the natural frequencies are also investigated.