Nonlinear dynamics of inplane loaded imperfect rectangular plates
Abstract
This paper deals with the nonlinear vibrations of composite laminated plates using the generalized formulation of which the von Karmantype formulation is a special case. The twodimensional 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 inplane applied edge loads have also been included in the analysis. Numerical examples for simplysupported plates indicate that for inplane loaded imperfect plates, the von Karman formulation differs slightly when compared with the present more general formulation.
 Publication:

ASME Journal of Applied Mechanics
 Pub Date:
 December 1992
 Bibcode:
 1992ATJAM..59..893B
 Keywords:

 Equilibrium Equations;
 Laminates;
 Plane Strain;
 Plate Theory;
 Reinforced Plates;
 Shear Strain;
 Cartesian Coordinates;
 Displacement;
 Free Vibration;
 Hamiltonian Functions;
 Nonlinear Equations;
 Structural Mechanics