Invariant torus and its destruction for an oscillator with dry friction

Xiaoming  Zhang; Chao  Zeng; Denghui Li; Jianhua  Xie; Celso Grebogi

doi:10.1007/s11071-021-06492-2

Invariant torus and its destruction for an oscillator with dry friction

Xiaoming Zhang, Chao Zeng, Denghui Li^* (Corresponding Author), Jianhua Xie, Celso Grebogi

^*Corresponding author for this work

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Abstract

Mechanical systems with dry friction are typical Filippov systems. Such class of systems have complicated dynamical behaviors due to the existence of sliding motion. In this work, we consider a one-degree-of-freedom oscillator with dry friction force. The phase map is derived to reduce the system to a circle map, and then the existence of forward invariant torus is proved under suitable assumptions. Moreover, the typical resonance phenomenon and the grazing bifurcation of invariant torus are discussed. We find that the destruction of invariant tori is due to a loss of transversality for sufficiently large perturbation, which is different from the usual smooth tori dynamics.

Original language	English
Pages (from-to)	3467–3477
Number of pages	11
Journal	Nonlinear Dynamics
Volume	104
Early online date	20 May 2021
DOIs	https://doi.org/10.1007/s11071-021-06492-2
Publication status	Published - 1 Jun 2021

Bibliographical note

Acknowledgments
This work is supported by the National Natural Science Foundation of China (11732014).

Keywords

dry friction oscillator
phase map
invariant torus
grazing-sliding bifurcation

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10.1007/s11071-021-06492-2

Zhang_etal_ND_Invariant_Torus_And_AAM
This is a post-peer-review, pre-copyedit version of an article published in Nonlinear Dynamics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11071-021-06492-2
Accepted author manuscript, 8.03 MBLicence: Unspecified

Cite this

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title = "Invariant torus and its destruction for an oscillator with dry friction",

abstract = "Mechanical systems with dry friction are typical Filippov systems. Such class of systems have complicated dynamical behaviors due to the existence of sliding motion. In this work, we consider a one-degree-of-freedom oscillator with dry friction force. The phase map is derived to reduce the system to a circle map, and then the existence of forward invariant torus is proved under suitable assumptions. Moreover, the typical resonance phenomenon and the grazing bifurcation of invariant torus are discussed. We find that the destruction of invariant tori is due to a loss of transversality for sufficiently large perturbation, which is different from the usual smooth tori dynamics.",

keywords = "dry friction oscillator, phase map, invariant torus, grazing-sliding bifurcation",

author = "Xiaoming Zhang and Chao Zeng and Denghui Li and Jianhua Xie and Celso Grebogi",

note = "Acknowledgments This work is supported by the National Natural Science Foundation of China (11732014).",

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doi = "10.1007/s11071-021-06492-2",

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T1 - Invariant torus and its destruction for an oscillator with dry friction

AU - Zhang, Xiaoming

AU - Zeng, Chao

AU - Li, Denghui

AU - Xie, Jianhua

AU - Grebogi, Celso

N1 - Acknowledgments This work is supported by the National Natural Science Foundation of China (11732014).

PY - 2021/6/1

Y1 - 2021/6/1

N2 - Mechanical systems with dry friction are typical Filippov systems. Such class of systems have complicated dynamical behaviors due to the existence of sliding motion. In this work, we consider a one-degree-of-freedom oscillator with dry friction force. The phase map is derived to reduce the system to a circle map, and then the existence of forward invariant torus is proved under suitable assumptions. Moreover, the typical resonance phenomenon and the grazing bifurcation of invariant torus are discussed. We find that the destruction of invariant tori is due to a loss of transversality for sufficiently large perturbation, which is different from the usual smooth tori dynamics.

AB - Mechanical systems with dry friction are typical Filippov systems. Such class of systems have complicated dynamical behaviors due to the existence of sliding motion. In this work, we consider a one-degree-of-freedom oscillator with dry friction force. The phase map is derived to reduce the system to a circle map, and then the existence of forward invariant torus is proved under suitable assumptions. Moreover, the typical resonance phenomenon and the grazing bifurcation of invariant torus are discussed. We find that the destruction of invariant tori is due to a loss of transversality for sufficiently large perturbation, which is different from the usual smooth tori dynamics.

KW - dry friction oscillator

KW - phase map

KW - invariant torus

KW - grazing-sliding bifurcation

U2 - 10.1007/s11071-021-06492-2

DO - 10.1007/s11071-021-06492-2

M3 - Article

SN - 0924-090X

VL - 104

SP - 3467

EP - 3477

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

ER -

Invariant torus and its destruction for an oscillator with dry friction

Abstract

Bibliographical note

Keywords

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