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
[1]  
[Anonymous], 1955, VIBRATIONS PROBLEMS
[2]  
[Anonymous], 1976, NUMERICAL METHOD FIN, DOI DOI 10.1002/NME.1620110913
[3]  
[Anonymous], 1970, Prikl Mat Mech
[4]   Dynamics of an elastic structure excited by harmonic and aharmonic impactor motions [J].
Balachandran, B .
JOURNAL OF VIBRATION AND CONTROL, 2003, 9 (3-4) :265-279
[5]   Some aspects of the dynamical behaviour of the impact force generator [J].
Blazejczyk-Okolewska, B ;
Czolczynski, K .
CHAOS SOLITONS & FRACTALS, 1998, 9 (08) :1307-1320
[6]   The effect of discretization on the numerical simulation of the vibrations of the impacting cantilever beam [J].
Blazejczyk-Okolewska, Barbara ;
Czolczynski, Krzysztof ;
Kapitaniak, T .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (10) :3073-3090
[7]   Hard versus soft impacts in oscillatory systems modeling [J].
Blazejczyk-Okolewska, Barbara ;
Czolczynski, Krzysztof ;
Kapitaniak, T .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (05) :1358-1367
[8]   Analysis of transitions between different ringing schemes of the church bell [J].
Brzeski, P. ;
Kapitaniak, T. ;
Perlikowski, P. .
INTERNATIONAL JOURNAL OF IMPACT ENGINEERING, 2015, 85 :57-66
[9]   GRAZING BIFURCATIONS IN IMPACT OSCILLATORS [J].
CHIN, W ;
OTT, E ;
NUSSE, HE ;
GREBOGI, C .
PHYSICAL REVIEW E, 1994, 50 (06) :4427-4444
[10]   Analytical and numerical investigations of stable periodic solutions of the impacting oscillator with a moving base [J].
Czolczynski, Krzysztof ;
Blazejczyk-Okolewska, Barbara ;
Okolewski, Andrzej .
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 2016, 115 :325-338
12345