Shear deformable versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates

In the present study, (i) the classical Von Kárman theory, (ii) the first-order shear deformation theory and (iii) the higher-order (third-order) shear deformation theory are compared for studying the nonlinear forced vibrations of isotropic and laminate composite rectangular plates. In particular, the harmonic response in the frequency neighborhood of the fundamental mode of rectangular plates is investigated and the response curves computed by using the three different theories are compared. The boundary conditions of the plates are simply supported with immovable edges. Geometric imperfections are taken into account. Calculations for isotropic and laminated composite plates are presented and results are discussed. For isotropic plates, the frequency-response curves for large-amplitude vibrations obtained by using the three theories are almost coincident. For laminated composite plates, differences arise for relatively thick plates (ratio between the thickness and the edge equal to 0.1), while for thin plates (ratio between the thickness and the edge equal to 0.01), no difference is obtained. For all cases, the first-order shear deformation (with shear correction factor 3/2) and the higher-order shear deformation theories give practically coincident results and differences are observed with respect to the classical Von Kárman theory.