BIFURCATIONS IN IMPACT OSCILLATIONS

被引：135
作者：
FOALE, S
BISHOP, SR
机构：
[1] Centre for Nonlinear Dynamics, Civil Engineering Building, University College London, London
来源：
NONLINEAR DYNAMICS | 1994年 / 6卷 / 03期
关键词：
IMPACT OSCILLATORS; BIFURCATIONS; GRAZING;
D O I：
10.1007/BF00053387
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
Models of impact oscillators using an instantaneous impact law are by their very nature discontinuous. These discontinuities give rise to bifurcations which cannot be classified using the usual tools of bifurcation analysis. However, we present numerical evidence which suggests that these discontinuous bifurcations are just the limits (in some sense) of standard bifurcations of smooth dynamical systems as the impact is hardened. Finally we show how one dimensional maps of the interval with essentially similar characteristics can exhibit the same kinds of bifurcational behaviour, and how these bifurcations are related to standard bifurcations.
引用
收藏
页码：285 / 299
页数：15
相关论文
共 13 条
[1]  
[Anonymous], 2012, PRACTICAL NUMERICAL
[2]  
BLOCK LS, 1991, LECTURE NOTES MATH, V1513
[3]   DYNAMIC COMPLEXITIES OF FORCED IMPACTING SYSTEMS [J].
FOALE, S ;
BISHOP, SR .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1992, 338 (1651) :547-556
[4]   GEOMETRICAL CONCEPTS AND COMPUTATIONAL TECHNIQUES OF NONLINEAR DYNAMICS [J].
FOALE, S ;
THOMPSON, JMT .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1991, 89 (1-3) :381-394
[5]  
Goldsmith W., 1960, IMPACT
[6]   NONPERIODIC MOTION CAUSED BY GRAZING-INCIDENCE IN AN IMPACT OSCILLATOR [J].
NORDMARK, AB .
JOURNAL OF SOUND AND VIBRATION, 1991, 145 (02) :279-297
[7]  
NORDMARK AB, 1992, THESIS ROYAL I TECHN
[8]   BORDER-COLLISION BIFURCATIONS INCLUDING PERIOD 2 TO PERIOD 3 FOR PIECEWISE SMOOTH SYSTEMS [J].
NUSSE, HE ;
YORKE, JA .
PHYSICA D-NONLINEAR PHENOMENA, 1992, 57 (1-2) :39-57
[9]   THE DYNAMICS OF A HARMONICALLY EXCITED SYSTEM HAVING RIGID AMPLITUDE CONSTRAINTS .2. CHAOTIC MOTIONS AND GLOBAL BIFURCATIONS [J].
SHAW, SW .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1985, 52 (02) :459-464
[10]   THE DYNAMICS OF A HARMONICALLY EXCITED SYSTEM HAVING RIGID AMPLITUDE CONSTRAINTS .1. SUBHARMONIC MOTIONS AND LOCAL BIFURCATIONS [J].
SHAW, SW .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1985, 52 (02) :453-458
12