Nonlinear vibration analysis of geometrically nonlinear shell structures

The nonlinear vibration analysis of a geometrically nonlinear shell structure is investigated in this study. In general, when the shell structure is subjected to excessive loadings, the large deformation of the shell structures must be considered, and the governing equation of the shell structure becomes nonlinear since the stiffness matrix of the governing equation is related to the deflection. Therefore, the natural frequency of the shell structure is varied with respect to the time which is quite different from that of the linear structures. In order to solve the nonlinearity of the governing equations of the shell structures, the well known Newton-Raphson iteration procedure in conjunction with Newmark scheme is adopted to perform the frequency analysis of the nonlinear-shell structures. Incidentally, the natural frequencies for various curvatures of the shell structures are also investigated from the practical engineering point of view.