Lyapunov exponents in discrete modelling of a cantilever beam impacting on a moving base

被引：18
作者：
Czolczynski, Krzysztof [1 ]
Okolewski, Andrzej [2 ]
Blazejczyk-Okolewska, Barbara [1 ]
机构：
[1] Lodz Univ Technol, Div Dynam, 1-15 Stefanowskiego St, Lodz, Poland
[2] Lodz Univ Technol, Inst Math, 215 Wolczanska St, Lodz, Poland
来源：
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2017年 / 88卷
关键词：
Impacting cantilever beam; Hertz's damp contact model; Periodic solution; Lyapunov exponents; SIDED ELASTIC CONSTRAINT; GRAZING BIFURCATIONS; PERIODIC-SOLUTIONS; LINEAR-OSCILLATOR; DYNAMICS; SYSTEM; MOTION; BEHAVIOR; CHAOS; SOFT;
D O I：
10.1016/j.ijnonlinmec.2016.10.015
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The dynamic behaviour of a cantilever beam of an unnegligible large mass and with a concentrated mass fixed at its end, which impacts on a movable base according to Hertz's damp law, is studied. A new finite element reference model of the system and its lower-dimensional substitutive models with one degree or two degrees of freedom are developed. The qualitative-type as well as quantitative-type applicability limits of these substitutive models are discussed - the latter ones are described in terms of the corresponding spectra of Lyapunov exponents.
引用
收藏
页码：74 / 84
页数：11
相关论文
共 48 条
[31]   NONPERIODIC MOTION CAUSED BY GRAZING-INCIDENCE IN AN IMPACT OSCILLATOR [J].
NORDMARK, AB .
JOURNAL OF SOUND AND VIBRATION, 1991, 145 (02) :279-297
[32]   TRANSITION TO CHAOTIC MOTION IN MECHANICAL SYSTEMS WITH IMPACTS [J].
PETERKA, F ;
VACIK, J .
JOURNAL OF SOUND AND VIBRATION, 1992, 154 (01) :95-115
[33]   Explanation of appearance and characteristics of intermittency chaos of the impact oscillator [J].
Peterka, F ;
Kotera, T ;
Cipera, S .
CHAOS SOLITONS & FRACTALS, 2004, 19 (05) :1251-1259
[34]   Behaviour of impact oscillator with soft and preloaded stop [J].
Peterka, F .
CHAOS SOLITONS & FRACTALS, 2003, 18 (01) :79-88
[35]  
Peterka F., 1981, INTRO VIBRATION MECH
[36]   Impact oscillator with Hertz's model of contact [J].
Pust, L ;
Peterka, F .
MECCANICA, 2003, 38 (01) :99-114
[37]   Mirror hysteresis and Lyapunov exponents of impact oscillator with symmetrical soft stops [J].
Serweta, Wioleta ;
Okolewski, Andrzej ;
Blazejczyk-Okolewska, Barbara ;
Czolczynski, Krzysztof ;
Kapitaniak, Tomasz .
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 2015, 101 :89-98
[38]   Lyapunov exponents of impact oscillators with Hertz's and Newton's contact models [J].
Serweta, Wioleta ;
Okolewski, Andrzej ;
Blazejczyk-Okolewska, Barbara ;
Czolczynski, Krzysztof ;
Kapitaniak, Tomasz .
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 2014, 89 :194-206
[39]   A PERIODICALLY FORCED IMPACT OSCILLATOR WITH LARGE DISSIPATION [J].
SHAW, SW ;
HOLMES, PJ .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1983, 50 (4A) :849-857
[40]   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
12345