Awrejcewicz, J.; Krysko, V. A. Feigenbaum scenario exhibited by thin plate dynamics. (English) Zbl 0980.74029 Nonlinear Dyn. 24, No. 4, 373-398 (2001). 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. Cited in 7 Documents MSC: 74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics 74K20 Plates 37N15 Dynamical systems in solid mechanics Keywords:Hopf bifurcation; algebraic equations; thin flexible isotropic plate; external load; period doubling bifurcations; chaotic dynamics; ordinary differential equations; Feigenbaum scenario PDFBibTeX XMLCite \textit{J. Awrejcewicz} and \textit{V. A. Krysko}, Nonlinear Dyn. 24, No. 4, 373--398 (2001; Zbl 0980.74029) Full Text: DOI