Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments

Large-amplitude (geometrically nonlinear) vibrations of rectangular plates subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances are investigated. The von Kármán nonlinear strain–displacement relationships are used. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite plate; geometric imperfections are taken into account. The nonlinear equations of motion are studied by using a code based on arclength continuation method that allows bifurcation analysis. Comparison of calculations to numerical results available in the literature is performed for simply supported plates with immovable and movable edges. Three different boundary conditions are considered and results are compared: (i) simply supported plates with immovable edges; (ii) simply supported plates with movable edges; and (iii) fully clamped plates. An experiment has been specifically performed in laboratory in order to very the accuracy of the present numerical model; a good agreement of theoretical and experimental results has been found for large-amplitude vibrations around the fundamental resonance of the aluminum plate tested.