Feigenbaum scenario exhibited by thin plate dynamics

被引：31
作者：
Awrejcewicz, J
Krysko, VA
机构：
[1] Lodz Tech Univ, Dept Automat & Biomech, PL-90924 Lodz, Poland
[2] Saratov State Univ, Dept Math, Saratov 410054, Russia
来源：
NONLINEAR DYNAMICS | 2001年 / 24卷 / 04期
关键词：
Hopf bifurcation; flexible plate; chaos;
D O I：
10.1023/A:1011133223520
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
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.
引用
收藏
页码：373 / 398
页数：26
相关论文
共 20 条
  • [11] KUKLIN PM, 1981, SELFWAVES PROCESSES
  • [12] Landa P. S., 1996, NONLINEAR OSCILLATIO
  • [13] Turbulence in nonclosed fluid flows as a noise-induced phase transition
    Landa, PS
    [J]. EUROPHYSICS LETTERS, 1996, 36 (06): : 401 - 406
  • [14] LANDA PS, 1995, PRIKLADNAYA NELINEYN, V2, P37
  • [15] Nayfeh A., 1979, NONLINEAR OSCILLATIO
  • [16] NAYFEH AH, 1989, APPL MECH REV, V42, P5175
  • [17] Sathyamoorthy M., 1987, APPL MECH REV, V40, P1553, DOI DOI 10.1115/1.3149544
  • [18] SCHUSTER HG, 1984, DETERMINISTICS CHAOS
  • [19] STOLIAROV NN, 1982, INVESTIGATION PLATES, P195
  • [20] Thompson J.M.T., 2002, Nonlinear dynamics and chaos
12