Nonlinear vibrations of thick laminated circular cylindrical panels

Geometrically nonlinear forced vibrations of thick, deep laminated circular cylindrical panels are studied via multi-modal energy approach based on Lagrange equations. It is assumed that the panel is subjected to a steady harmonic concentrated force acting in the radial direction. Simply supported movable boundary conditions are considered and the energy functional is reduced to a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms using admissible eigenfunctions. A code based on pseudo arc-length continuation and collocation method is used to carry out a bifurcation analysis and obtain numerical solutions. Several internal resonances are detected. Direct time integration of the equations of motion has also been performed to obtain the bifurcation diagrams and Poincaré maps. It is shown that the panel exhibits complex nonlinear dynamics including quasi-periodic, intermittency and chaos in the vicinity of internal resonances. Moreover, it is illustrated that the choice of Amabili–Reddy higher-order shear deformation theory could be recommended for studying deep and thick panels.