Influence of the Aspect Ratio on the Dynamic Stability and Nonlinear Response of Rectangular Plates

The dynamic stability and nonlinear response of simply-supported rectangular plates subjected to parametric excitation are investigated. The large-deflection plate theory used in the analysis is derived in terms of the stress function F and lateral displacement w and is applied to rectangular plates with stress-free supported edges and uniformly stressed loaded edges. General rectangular plates are considered, the aspect ratio of the plate being regarded as an additional parameter of the system. Calculations are carried out for rectangular plates of various aspect ratios, and the relative importance of the principal regions of parametric instability associated with the lower mode shapes is clarified. The stationary response of the system within a principal region of instability is also evaluated. The results obtained indicate that the aspect ratio plays a crucial role in determining the stability of rectangular plates; elongated plates are more susceptible to various parametric resonances than square plates.