Feigenbaum scenario exhibited by thin plate dynamics

The dimensionless partial differential equations governing the dynamics of a thin flexible isotropic plate with an external load are derived and investigated. The period doubling bifurcations, as well as the chaotic dynamics, are detected and analyzed. The algorithms leading to the reduction of the original equations to those of a difference set of ordinary differential and algebraic equations are proposed, compared to other known methods, and then applied to the problem. Among others, it is shown that, in spite of the system complexity, the Feigenbaum scenario exhibited by one-dimensional maps also governs the route to chaos in the continuous system under consideration.