Analysis of circular cylindrical shells under harmonic forces

A generalized thin shell theory for the stress-deformation analysis of thin-walled circular cylindrical shells is formulated based on the Hamilton's variational principle. The theory is applicable to multiple in-phase and out-of-phase harmonic forces and general boundary conditions. The stationary conditions of the Hamilton functional are then evoked to recover the equations of motion and boundary conditions of the problem. The unknown displacement fields are expanded as infinite complex Fourier series in the circumferential coordinate. The resulting field equations are observed to couple the radial, tangential and longitudinal displacement contributions within each mode, while uncoupling the contributions of a given Fourier mode from those of other Fourier modes. A general solution for the obtained field equations is developed for harmonic loading of general spatial distribution. The method developed is verified against well established solutions and its applicability to practical problems is illustrated through examples.