Forced large amplitude periodic vibrations of cylindrical shallow shells

Forced, large amplitude, periodic vibrations of open, linear elastic and isotropic, cylindrical shells are studied. A p-version finite element, which is derived following first-order shear deformation theory, is employed to define the model and an algorithm based on the shooting and Newton methods is used to solve the equations of motion. The influences that the amplitude and spatial distribution of the external excitation, the curvature to width ratio and the shell's thickness have on the dynamic response are investigated. To characterize the geometrically non-linear oscillations time plots, phase planes and Fourier spectra are employed. To characterize the stability of the solutions the Floquet multipliers are computed. Responses with even and odd harmonics to purely harmonic excitations and strong modal interactions due to the non-linearity of the system are found. The methods proposed constitute a good alternative to analyse geometrically non-linear periodic vibrations of shells because the number of approximations is reduced and the computational cost is, although significant, reasonable.