Analytical and numerical investigations of stable periodic solutions of the impacting oscillator with a moving base

被引：23

作者：

Czolczynski, Krzysztof ^{[1
]}

Blazejczyk-Okolewska, Barbara ^{[1
]}

Okolewski, Andrzej ^{[2
]}

机构：

[1] Lodz Univ Technol, Div Dynam, 1-15 Stefanowskiego Str, Lodz, Poland

[2] Lodz Univ Technol, Inst Math, 215 Wolczanska Str, Lodz, Poland

来源：

INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES | 2016年 / 115卷

关键词：

Impact oscillator; Time-varying amplitude constraint; Stable periodic solutions; Lyapunov exponents; Hard versus soft impact; SIDED ELASTIC CONSTRAINT; LYAPUNOV EXPONENTS; MECHANICAL SYSTEMS; FORCED SYSTEM; BIFURCATION-ANALYSIS; DYNAMICS; CLEARANCE; DIVERSITY; MOTIONS; ATTRACTORS;

D O I：

10.1016/j.ijmecsci.2016.07.004

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

A vibrating system with impacts that can be used as a model of the cantilever beam with a mass at its end impacting against a harmonically moving frame is investigated. An analytical method, based on Peterka's approach, to obtain stable periodic solutions to the equations of motion is presented. The results of analytical investigations have been compared to the results of numerical simulations conducted for two different, equivalent as far as the impact energy dissipation extent is concerned, ways of modelling of impacts. The ranges of existence of stable periodic solutions, determined analytically and numerically with bifurcation diagrams of spectra of Lyapunov exponents, show excellent conformity. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：325 / 338

页数：14

共 43 条

[1] PERIODIC AND CHAOTIC BEHAVIOR OF A THRESHOLD-LIMITED 2-DEGREE-OF-FREEDOM SYSTEM
AIDANPAA, JO
GUPTA, RB
[J]. JOURNAL OF SOUND AND VIBRATION, 1993, 165 (02) : 305 - 327
[2] Numerical simulation of the soft contact dynamics of an impacting bilinear oscillator
Andreaus, Ugo
Placidi, Luca
Rega, Giuseppe
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (09) : 2603 - 2616
[3] Benettin G., 1980, Meccanica, V15, P9, DOI [DOI 10.1007/BF02128236, 10.1007/BF02128236]
[4] Some aspects of the dynamical behaviour of the impact force generator
Blazejczyk-Okolewska, B
Czolczynski, K
[J]. CHAOS SOLITONS & FRACTALS, 1998, 9 (08) : 1307 - 1320
[5] Determination of geometrical conditions of assembly and impacts in classified types of mechanical systems with impacts
Blazejczyk-Okolewska, B
Czolczynski, K
Kapitaniak, T
[J]. EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, 2005, 24 (02) : 277 - 291
[6] Classification principles of types of mechanical systems with impacts - fundamental assumptions and rules
Blazejczyk-Okolewska, B
Czolczynski, K
Kapitaniak, T
[J]. EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, 2004, 23 (03) : 517 - 537
[7] Blazejczyk-Okolewska B., 2013, MATH PROBL ENG
[8] Hard versus soft impacts in oscillatory systems modeling
Blazejczyk-Okolewska, Barbara
Czolczynski, Krzysztof
Kapitaniak, T
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (05) : 1358 - 1367
[9] GRAZING BIFURCATIONS IN IMPACT OSCILLATORS
CHIN, W
OTT, E
NUSSE, HE
GREBOGI, C
[J]. PHYSICAL REVIEW E, 1994, 50 (06) : 4427 - 4444
[10] On the existence of a stable periodic solution of an impacting oscillator with two fenders
Czolczynski, K
Kapitaniak, T
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2004, 14 (09): : 3115 - 3134

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