Nonlinear vibrations and multiple resonances of fluid filled arbitrary laminated circular cylindrical shells

Nonlinear forced vibrations of water-filled, laminated circular cylindrical shells are studied by using the Amabili–Reddy nonlinear higher-order shear deformation theory and energy approach in the Lagrangian description. The fluid is modeled by potential flow. It is assumed that the shell is subjected to a steady harmonic concentrated force acting in the radial direction. Pseudo arc-length continuation and collocation technique is used to carry out bifurcation analysis and to obtain nonlinear frequency–amplitude responses. Direct time integration of the equations of motion has also been performed by using Gear’s backward differentiation formula (BDF) to obtain time histories, phase space diagrams and Poincaré maps. The effect of internal fluid and lamination angle on the frequency–amplitude response in the neighborhood of the resonance frequency, traveling wave solution and internal resonances of simply supported shells are investigated. It is shown that water-filled composite shells may exhibit complex nonlinear dynamics including a rare and intricate 1:1:1:1 internal resonance.