Global dynamics of a harmonically excited oscillator with a play: Numerical studies

Antonio S. E.  Chong; Yue Yuan; Ekaterina Pavlovskaia; Marian Wiercigroch

doi:10.1016/j.ijnonlinmec.2017.03.015

Global dynamics of a harmonically excited oscillator with a play: Numerical studies

Antonio S. E. Chong, Yue Yuan, Ekaterina Pavlovskaia, Marian Wiercigroch

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Abstract

In this paper a harmonically excited linear oscillator with a play is investigated. Direct numerical simulation and numerical continuation techniques were employed to study the system behaviour. To conduct the numerical analysis, the system differential equations were transformed into the autonomous form
and were then solved using our newly developed in-house Matlab-based computational suite ABESPOL [1]. The results are presented in form of trajectories and Poincaré maps on the phase plane, bifurcation diagrams and basins of attraction. The bifurcation analysis was supported by a path following method. The influence of each system parameter (except gap) on the system dynamics was studied in detail. The bifurcations known as interior crisis and boundary crisis were observed and discussed in this work. Notably, the parameter regions where various types of grazing induced bifurcations occurred were detected and investigated.

Original language	English
Pages (from-to)	98-108
Number of pages	11
Journal	International Journal of Non-Linear Mechanics
Volume	94
Early online date	19 Mar 2017
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2017.03.015
Publication status	Published - Sept 2017

Bibliographical note

This work was supported by the National Secretariat of Science, Technology and Innovation of Ecuador (SENESCYT); the Escuela Superior Politécnica del Litoral of Ecuador (ESPOL); the National Natural Science Foundation of China (11272268, 11572263) and Scholarship of China. A.S.E. Chong and Y. Yue acknowledge the hospitality of the Centre of Applied Dynamics Research at the University of Aberdeen.

Keywords

Non-smooth systems
Backlash
Clearance
Impacts
Numerical simulation
Path following
Bifurcation analysis

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10.1016/j.ijnonlinmec.2017.03.015Licence: Unspecified

Accepted Manuscript
© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 12.6 MBLicence: CC BY-NC-ND

Cite this

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title = "Global dynamics of a harmonically excited oscillator with a play: Numerical studies",

abstract = "In this paper a harmonically excited linear oscillator with a play is investigated. Direct numerical simulation and numerical continuation techniques were employed to study the system behaviour. To conduct the numerical analysis, the system differential equations were transformed into the autonomous formand were then solved using our newly developed in-house Matlab-based computational suite ABESPOL [1]. The results are presented in form of trajectories and Poincar{\'e} maps on the phase plane, bifurcation diagrams and basins of attraction. The bifurcation analysis was supported by a path following method. The influence of each system parameter (except gap) on the system dynamics was studied in detail. The bifurcations known as interior crisis and boundary crisis were observed and discussed in this work. Notably, the parameter regions where various types of grazing induced bifurcations occurred were detected and investigated.",

keywords = "Non-smooth systems, Backlash, Clearance, Impacts, Numerical simulation, Path following , Bifurcation analysis",

author = "Chong, {Antonio S. E.} and Yue Yuan and Ekaterina Pavlovskaia and Marian Wiercigroch",

note = "This work was supported by the National Secretariat of Science, Technology and Innovation of Ecuador (SENESCYT); the Escuela Superior Polit{\'e}cnica del Litoral of Ecuador (ESPOL); the National Natural Science Foundation of China (11272268, 11572263) and Scholarship of China. A.S.E. Chong and Y. Yue acknowledge the hospitality of the Centre of Applied Dynamics Research at the University of Aberdeen.",

year = "2017",

month = sep,

doi = "10.1016/j.ijnonlinmec.2017.03.015",

language = "English",

volume = "94",

pages = "98--108",

journal = "International Journal of Non-Linear Mechanics",

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TY - JOUR

T1 - Global dynamics of a harmonically excited oscillator with a play

T2 - Numerical studies

AU - Chong, Antonio S. E.

AU - Yuan, Yue

AU - Pavlovskaia, Ekaterina

AU - Wiercigroch, Marian

N1 - This work was supported by the National Secretariat of Science, Technology and Innovation of Ecuador (SENESCYT); the Escuela Superior Politécnica del Litoral of Ecuador (ESPOL); the National Natural Science Foundation of China (11272268, 11572263) and Scholarship of China. A.S.E. Chong and Y. Yue acknowledge the hospitality of the Centre of Applied Dynamics Research at the University of Aberdeen.

PY - 2017/9

Y1 - 2017/9

N2 - In this paper a harmonically excited linear oscillator with a play is investigated. Direct numerical simulation and numerical continuation techniques were employed to study the system behaviour. To conduct the numerical analysis, the system differential equations were transformed into the autonomous formand were then solved using our newly developed in-house Matlab-based computational suite ABESPOL [1]. The results are presented in form of trajectories and Poincaré maps on the phase plane, bifurcation diagrams and basins of attraction. The bifurcation analysis was supported by a path following method. The influence of each system parameter (except gap) on the system dynamics was studied in detail. The bifurcations known as interior crisis and boundary crisis were observed and discussed in this work. Notably, the parameter regions where various types of grazing induced bifurcations occurred were detected and investigated.

AB - In this paper a harmonically excited linear oscillator with a play is investigated. Direct numerical simulation and numerical continuation techniques were employed to study the system behaviour. To conduct the numerical analysis, the system differential equations were transformed into the autonomous formand were then solved using our newly developed in-house Matlab-based computational suite ABESPOL [1]. The results are presented in form of trajectories and Poincaré maps on the phase plane, bifurcation diagrams and basins of attraction. The bifurcation analysis was supported by a path following method. The influence of each system parameter (except gap) on the system dynamics was studied in detail. The bifurcations known as interior crisis and boundary crisis were observed and discussed in this work. Notably, the parameter regions where various types of grazing induced bifurcations occurred were detected and investigated.

KW - Non-smooth systems

KW - Backlash

KW - Clearance

KW - Impacts

KW - Numerical simulation

KW - Path following

KW - Bifurcation analysis

U2 - 10.1016/j.ijnonlinmec.2017.03.015

DO - 10.1016/j.ijnonlinmec.2017.03.015

M3 - Article

SN - 0020-7462

VL - 94

SP - 98

EP - 108

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

ER -

Global dynamics of a harmonically excited oscillator with a play: Numerical studies

Abstract

Bibliographical note

Keywords

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