A modified variational approach for vibration analysis of ring-stiffened conical–cylindrical shell combinations

This work presents a modified variational method for dynamic analysis of ring-stiffened conical–cylindrical shells subjected to different boundary conditions. The method involves partitioning of the stiffened shell into appropriate shell segments in order to accommodate the computing requirement of high-order vibration modes and responses. All essential continuity constraints on segment interfaces are imposed by means of a modified variational principle and least-squares weighted residual method. Reissner-Naghdi's thin shell theory combined with the discrete element stiffener theory to consider the ring-stiffening effect is employed 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 segment. To test the convergence, efficiency and accuracy of the present method, both free and forced vibrations of non-stiffened and stiffened shells are examined under different combinations of edge support conditions. Two types of external excitation forces are considered for the forced vibration analysis, i.e., the axisymmetric line force and concentrated point force. The numerical results obtained from the present method show good agreement with previously published results and those from the finite element program ANSYS. Effects of structural damping on the harmonic vibration responses of the stiffened conical–cylindrical–conical shell are also presented.

► A variational method is proposed for vibration analysis of ring-stiffened conical–cylindrical shells. ► Free and forced vibrations of non-stiffened and stiffened shells are examined. ► Effects of structural damping on harmonic vibration responses are presented. ► The present solutions are efficient, robust and accurate.