Non-Linear Vibrations of Shells

Large-amplitude (geometrically nonlinear) vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated. The Lagrange equations of motion are obtained by an energy approach, retaining damping through Rayleigh's dissipation function. Four different nonlinear thin shell theories, namely Donnell's, Sanders-Koiter, Flfigge-Lur'e-Byrne and Novozhilov's theories, are used to calculate the elastic strain energy. These theories neglect rotary inertia and shear deformation. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite shells. The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of the lowest natural frequency is computed for all these shell theories. Numerical responses obtained by using these four nonlinear shell theories are also compared to results obtained by using the Donnell's nonlinear shallow-shell equation of motion. A validation of calculations by comparison to experimental results is also performed. Both empty and fluid-filled shells are investigated by using a potential fluid model. Boundary conditions for simply supported shells are exactly satisfied. Different expansions involving from 14 to 48 generalized coordinates, associated to natural modes of simply supported shells, are used. The nonlinear equations of motion are studied by using a code based on the arclength continuation method that allows bifurcation analysis.