Nonlinear Vibration Analysis of Simply Supported Stiffened Plate by a Variational Method

Large-amplitude free vibration analysis of uni-axially single stiffened rectangular plates subjected to transverse loading with simply supported boundary conditions has been presented. The mathematical formulation is based on energy principle. Geometric nonlinearity is accounted for by consideration of nonlinear strain-displacement relations. The static problem is solved through an iterative scheme and the dynamic problem is solved with the static displacement field as an initial guess. Influence of stiffener position, plate aspect ratio, and stiffener to plate thickness ratio on the large amplitude dynamic behavior has been studied. The dynamic behavior has been furnished in the form of backbone curves in a dimensionless frequency-amplitude plane.