Effects of modal coupling on the nonlinear dynamics of hyperelastic circular cylindrical shells

The nonlinear dynamics of a simply supported circular cylindrical shell is analyzed using an analytical model that considers both physical and geometric nonlinearities. The material that composes the shell is assumed as homogeneous, isotropic, hyperelastic and incompressible, being described by the Mooney-Rivlin hyperelastic constitutive law. The geometric nonlinearity is introduced into the analytical model by applying the Sanders-Koiter’s nonlinear shell theory. The Rayleigh-Ritz method and Hamilton's principle are employed to obtain the nonlinear equilibrium equations. For that, the energy density function is expanded in Taylor series up to the fourth order and the transversal displacement field is described in Fourier series that considers both asymmetric and axisymmetric modes. This works focusses on evaluating the influence of the asymmetric and axisymmetric modes, selected in the modal solution of the transversal displacement field, on the frequency-amplitude relationships of the shell and resonance curves. It can be observed that the asymmetric modes provoke nonlinear hardening behavior of the hyperelastic shell. On the other hand, when the axisymmetric modes are added, there is a significant change in the nonlinear behavior of the hyperelastic shell - which indicates the importance of this modal coupling in the nonlinear dynamic analysis.