APPLICATION OF VARIATIONAL EQUATION OF MOTION TO THE NONLINEAR ANALYSIS OF DYNAMIC BUCKLING,

An integrated procedure has been proposed for applying the variational equation of motion to the analysis of nonlinear vibrations of solids. In this paper the procedure is extended to the analysis of nonlinear dynamic buckling. Example is given for a simply supported sandwich or homogeneous plate in plane-strain motion, one edge of which is fixed and the other subjected to a longitudinally oscillating displacement. Response curves for the parametrically excited, lateral vibration corresponding to the first instability region are presented. Results show that the transverse shear effect cannot be neglected for the sandwich plate, as in the case of ordinary, nonlinear lateral vibration of the plate. The transverse shear effect is, however, negligible for the homogeneous plate Timoshenko beam, at least for the first instability region. Author