Abstract Summary
In this work, Koiter’s theory is applied to study the nonlinear large amplitude vibrations of simply supported shallow spherical panels. The nonlinear equations of motion are determined by using the Rayleigh-Ritz method in an energetic approach. The displacement fields are approximated using an expansion of trigonometric functions that satisfy the boundary conditions. Therefore, the backbone curves are determined using multiple shooting method and an Euler-Newtonian predictor-corrector continuation algorithm and the Floquet theory is applied to determine the stability of nonlinear solutions. The obtained backbone curves show multiple internal resonances due to the coupling between nonlinear normal modes. Time responses of some points of the backbone curves are depicted to analyse the internal resonances, which can represent loss of stability and sudden changes in the structural behaviour of shells submitted by external forces.
