Abstract
In this paper, we study the non-linear stability of simply supported rectangular plates on a non-linear elastic foundation and use the theory of singularities to analyse the effect of the coefficients of the foundation on the stability behaviour. The results point out that the instability behaviour of the rectangular plate near a double eigenvalue is very complex due to the interaction between the foundation and plate. And the stability behaviour of the plate not only depends on the elastic coefficients of the foundation but also the modes of the plate when it losses its stability. From 45 bifurcation diagrams given in the paper, one can see that the rectangular plate not only occurs the secondary bifurcation but also has very complex super-critical behaviour like mode jumping. In these figures, we still discover the new manners of mode transition. Finally, we discuss all possible bifurcation behaviours of rectangular plates.
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