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Feigenbaum scenario exhibited by thin plate dynamics. (English) Zbl 0980.74029

Summary: We derive and investigate dimensionless partial differential equations governing the dynamics of thin flexible isotropic plate with external load. The period doubling bifurcations, as well as the chaotic dynamics, are analyzed. The algorithms leading to the reduction of the original equations to 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.

MSC:

74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics
74K20 Plates
37N15 Dynamical systems in solid mechanics
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