Analytical Model for Predicting Nonlinear Random and Snap-through Response of Buckled Plates

This paper presents a simplified model for predicting the nonlinear random response of flat and buckled plates. Based on a single mode representation of vibration response, r.m.s. values of the strain response to broadband excitation are evaluated for different static buckled configurations using the equivalent linearization technique. The dynamic effects on the overall strain response due to instability motion of snap-through are included. Parametric studies are performed in which the influences of the clamped and simply-supported boundaries, aspect ratio of the plate, thickness and length of the plate are considered. Using a simple single-model formula, the results of dynamic buckling motion were compared with finite-element models as well as experimental results. The comparisons between analytical results and experimental results help to assess the accuracy of the theory and the conditions under which deviations from the theory due to effects of imperfection and higher modes are significant. It is found that the theoretical model is useful for design and checking of computer results for curved plates in a slightly deflected form (initial deflection less than twice the thickness of plate) and the prediction accuracy on nonlinear analysis is higher than existing design formula based on linear response.