Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories

The geometrically nonlinear forced vibrations of laminated circular cylindrical shells are studied by using the Amabili–Reddy higher-order shear deformation theory. An energy approach based on Lagrange equations, retaining modal damping, is used in order to obtain the equations of motion. An harmonic point excitation is applied in radial direction and simply supported boundary conditions are assumed. The equations of motion are studied by using the pseudo-arclength continuation method and bifurcation analysis. A one-to-one internal resonance is always present for a complete circular cylindrical shell, giving rise to pitchfork bifurcations of the nonlinear response with appearance of a second branch with travelling wave response and quasi-periodic vibrations. The numerical results obtained by using the Amabili–Reddy shell theory are compared to those obtained by using an higher-order shear deformation theory retaining only nonlinear term of von Kármán type and the Novozhilov classical shell theory.

► Comparison of nonlinear shell theories with shear deformation.
► Amabili–Reddy higher-order shear deformation theory including all nonlinear terms.
► Nonlinear forced vibrations of circular cylindrical shells complete around the circumference.
► Pitchfork and Neimark–Sacker bifurcations giving travelling-wave and quasi-periodic responses, respectively.
► For thick laminated shells, the Amabili–Reddy theory should be used in order to have accurate results.