Vibration characteristics analysis of an elastically restrained cylindrical shell with arbitrary thickness variation

Abstract

A novel and unified solution is established to investigate the vibration characteristics of circular cylindrical shells with arbitrary variable thickness and general boundary conditions. Energy equation based on Donnell–Mushtari shell theory is formulated, with a modified Fourier series utilized for the construction of radial, circumferential and longitudinal displacements of shell structure, in which the auxiliary terms are introduced to tackle with differential discontinuity associated with elastic boundary restraints. Arbitrary thickness function is invariantly expanded into Fourier series to compress thickness variation information into Fourier coefficients accordingly. The proposed model is validated through the comparisons with those in the literature or finite element method. Excellent convergence can be observed with several truncated terms of modified Fourier series. Natural frequencies of a circular cylindrical shell with linearly varying thickness and constant mass decrease for constrained boundary conditions, and the distribution of modal displacement moves to the thinner side as the slope ratio increases. Axial thickness variation has more significant influence on natural frequencies of a step-wise cylindrical shell compared with that in circumferential direction.