Nonlinear curvature-based model and resonant finite-amplitude vibrations of symmetric cross-ply laminates

Moving from a general plate theory, a modified general classical laminated plate theory (MGCLPT) exhibiting nonlinear curvatures but still allowing for some worth features of linear curvature models (von Karman) is formulated. Starting from MGCLPT partial differential equations, a minimal discretized model suitable for the analysis of resonant finite-amplitude vibrations of symmetric cross-ply laminates, with immovable or movable supports, is obtained via the Galerkin procedure. Periodic responses of a single-mode model and of a 3:1 internally resonant two-mode model excited at primary resonance are obtained via the multiple time scale method. The influence of various system parameters (thickness ratio, plate aspect, number of laminae, kind of material, mode number) is addressed, and the comparison of nonlinear vibration results as obtained with the MGCLPT and the von Karman models for different boundary conditions shows some interesting differences.