Effects of a low frequency parametric excitation

被引:20
作者
Lakrad, F [1 ]
Schiehlen, W [1 ]
机构
[1] Univ Stuttgart, Inst B Mech, D-70550 Stuttgart, Germany
关键词
D O I
10.1016/j.chaos.2004.03.029
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The effects of a slowly varying parametric excitation on a shallow arch model are investigated. The delay bifurcation and he sequence of visited equilibria are analyzed, The method of Melnikov and a method proposed by Berglund [Adiabatic dynamical systems and hysteresis, Ph.D. thesis, Institut de Physique Theorique EPRFL, Lausanne, Switzerland, 1998] are used to determine chaotic regions. (C) 2004 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1149 / 1164
页数:16
相关论文
共 24 条
[1]  
BAJAJ AK, 1999, P IUTAM S NEW APPL N, P13
[2]   GENERALIZATION OF METHOD OF AVERAGING FOR SYSTEMS WITH 2 TIME SCALES [J].
BALACHANDRA, M ;
SETHNA, PR .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1975, 58 (03) :261-283
[3]   Memory effects and scaling laws in slowly driven systems [J].
Berglund, N ;
Kunz, H .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1999, 32 (01) :15-39
[4]  
BERGLUND N, 1998, THESIS I PHYS THEEOR
[5]  
Bogoliubov NN., 1961, Asymptotic methods in the theory of non-linear oscillations (In Russian)
[6]  
Engstler C, 1997, COMPUTING, V58, P173, DOI 10.1007/BF02684438
[7]  
GOLUBITSKY M, 2001, GLOBAL ANAL DYNAMICA
[8]   Slow passage through the nonhyperbolic homoclinic orbit associated with a subcritical pitchfork bifurcation for Hamiltonian systems and the change in action [J].
Haberman, R .
SIAM JOURNAL ON APPLIED MATHEMATICS, 2001, 62 (02) :488-513
[9]   SLOWLY VARYING JUMP AND TRANSITION PHENOMENA ASSOCIATED WITH ALGEBRAIC BIFURCATION PROBLEMS [J].
HABERMAN, R .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1979, 37 (01) :69-106
[10]  
Hairer E., 1993, SPRINGER SERIES COMP, V8