Nonlinear Vibrations of Rectangular Laminated Composite Plates With Different Boundary Conditions

Nonlinear vibrations of rectangular laminated composite plates with different boundary conditions are studied by using different nonlinear plate theories. In particular, numerical results for (i) the classical Von Kárman theory, (ii) the first_order shear deformation theory (SDT), and (iii) the third-order SDT are compared. The nonlinear response to harmonic excitation in the frequency neighborhood of the fundamental mode is investigated. Numerical investigation is carried out by using pseudo-arclength continuation method and bifurcation analysis. The boundary conditions of the plates are: simply supported with movable edges, simply supported with immovable edges, and clamped (CL) edges. For thick plates (thickness ratio 0.1), the strongest hardening nonlinear behavior is observed for CL plates, while the simply supported movable plates are the ones with the weakest nonlinearity among the three different boundary conditions studied here. Differences among the three nonlinear plate theories are large for thick laminated plates. For all the other cases, the first_order SDT, with shear correction factor [Formula: see text], and the higher-order SDT give almost coincident results.