Nonlinear dynamics of in-plane loaded imperfect rectangular plates

This paper deals with the nonlinear vibrations of composite laminated plates using the generalized formulation of which the von Karman-type formulation is a special case. The two-dimensional plate theory used is that of a parabolic shear theory in which the transverse shear strain distribution is parabolic across the plate thickness. The resulting governing equations of this formulation are nonlinear in all the plate displacement parameters unlike the von Karman model in which they are nonlinear in the lateral displacement only. Because of this complex nature of the equations the usual approach for nonlinear plate analysis cannot be used, and hence a regular perturbation technique has been adopted to obtain the solution of these equations. All the complexities like the initial imperfections and in-plane applied edge loads have also been included in the analysis. Numerical examples for simply-supported plates indicate that for in-plane loaded imperfect plates, the von Karman formulation differs slightly when compared with the present more general formulation.