A general approach for free vibration analysis of spinning joined conical–cylindrical shells with arbitrary boundary conditions

This paper presents a general approach for free vibration analysis of spinning local elastic-foundation supported joined conical–cylindrical shells (JCCSs) with arbitrary boundary conditions. The Donnell’s shell theory is employed in the modeling of the structures, and all the effects of centrifugal forces, Coriolis forces as well as initial hoop tensions are considered. The approach utilizes the concept of artificial springs which permit convenient joining of the conical and cylindrical shells. Particularly, it can efficiently simulate arbitrary boundary conditions of JCCSs. The spinning JCCSs are locally or completely surrounded by elastic foundation, formulated by the Pasternak model. By using the orthogonal polynomial series as the admissible functions, the frequency equations of spinning JCCSs with arbitrary boundary conditions are derived using the Rayleigh–Ritz method. Then, some numerical examples are compared with the available literature and finite element results to validate the present approach. Finally, the effects of key parameters on free vibration characteristics are investigated including spring stiffness, spinning speed, cone angle and local elastic foundation.