Nonlinear vibrations and stability of laminated shells using a modified first-order shear deformation theory

An original and consistent first-order shear deformation theory that retains all the nonlinear terms in the in-plane displacements and rotations is presented here. The theory is developed for dynamics and is applied to study large-amplitude, geometrically nonlinear vibrations. The numerical application to a simply supported, composite laminated circular cylindrical shell is implemented for illustration and validation purposes. Initially the theory is compared to an accurate third-order nonlinear shear deformation theory for the case of pressurized shell. This comparison validates the theory for buckling, which arises in case of external pressure, and post-buckling. The pressure is accurately modelled as displacement-dependent. Then, the nonlinear vibrations due to harmonic forcing around a resonance are studied in detail. The coupling between driven and companion mode gives a chaotic oscillation region near the linear resonance associated to a travelling-wave vibration. Results are presented in the frequency and time domains, in addition to sections of Poincaré maps.