Estimation of Lyapunov exponents for a system with sensitive friction model

Jerzy Wojewoda; Andrzej Stefanski; Marian Wiercigroch; Tomasz Kapitaniak

doi:10.1007/s00419-008-0291-9

Estimation of Lyapunov exponents for a system with sensitive friction model

Jerzy Wojewoda, Andrzej Stefanski, Marian Wiercigroch, Tomasz Kapitaniak

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

Mathematical modelling and numerical analysis of a vibrating system with dry friction is presented. Three qualitatively different friction characteristics are considered. One of them is an example of so-called sensitive friction characteristic. Their influence on the dynamics on the attractor of the friction oscillator is investigated through bifurcational analysis. This analysis is supported by Lyapunov exponents estimated using approach for the systems with discontinuities. Theoretical background for such a synchronisation-based method of determining the largest Lyapunov exponent is explained. The results obtained through the proposed approach approximate the LLE with a good precision.

Original language	English
Pages (from-to)	667–677
Number of pages	11
Journal	Archive of Applied Mechanics
Volume	79
Issue number	6
DOIs	https://doi.org/10.1007/s00419-008-0291-9
Publication status	Published - Jul 2009

Access to Document

10.1007/s00419-008-0291-9Licence: Unspecified

Cite this

@article{6cf382a608f04bd69a17ef194c030267,

title = "Estimation of Lyapunov exponents for a system with sensitive friction model",

abstract = "Mathematical modelling and numerical analysis of a vibrating system with dry friction is presented. Three qualitatively different friction characteristics are considered. One of them is an example of so-called sensitive friction characteristic. Their influence on the dynamics on the attractor of the friction oscillator is investigated through bifurcational analysis. This analysis is supported by Lyapunov exponents estimated using approach for the systems with discontinuities. Theoretical background for such a synchronisation-based method of determining the largest Lyapunov exponent is explained. The results obtained through the proposed approach approximate the LLE with a good precision.",

author = "Jerzy Wojewoda and Andrzej Stefanski and Marian Wiercigroch and Tomasz Kapitaniak",

year = "2009",

month = jul,

doi = "10.1007/s00419-008-0291-9",

language = "English",

volume = "79",

pages = "667–677",

journal = "Archive of Applied Mechanics",

issn = "0939-1533",

publisher = "Springer Verlag",

number = "6",

}

TY - JOUR

T1 - Estimation of Lyapunov exponents for a system with sensitive friction model

AU - Wojewoda, Jerzy

AU - Stefanski, Andrzej

AU - Wiercigroch, Marian

AU - Kapitaniak, Tomasz

PY - 2009/7

Y1 - 2009/7

N2 - Mathematical modelling and numerical analysis of a vibrating system with dry friction is presented. Three qualitatively different friction characteristics are considered. One of them is an example of so-called sensitive friction characteristic. Their influence on the dynamics on the attractor of the friction oscillator is investigated through bifurcational analysis. This analysis is supported by Lyapunov exponents estimated using approach for the systems with discontinuities. Theoretical background for such a synchronisation-based method of determining the largest Lyapunov exponent is explained. The results obtained through the proposed approach approximate the LLE with a good precision.

AB - Mathematical modelling and numerical analysis of a vibrating system with dry friction is presented. Three qualitatively different friction characteristics are considered. One of them is an example of so-called sensitive friction characteristic. Their influence on the dynamics on the attractor of the friction oscillator is investigated through bifurcational analysis. This analysis is supported by Lyapunov exponents estimated using approach for the systems with discontinuities. Theoretical background for such a synchronisation-based method of determining the largest Lyapunov exponent is explained. The results obtained through the proposed approach approximate the LLE with a good precision.

U2 - 10.1007/s00419-008-0291-9

DO - 10.1007/s00419-008-0291-9

M3 - Article

SN - 0939-1533

VL - 79

SP - 667

EP - 677

JO - Archive of Applied Mechanics

JF - Archive of Applied Mechanics

IS - 6

ER -

Estimation of Lyapunov exponents for a system with sensitive friction model

Abstract

Access to Document

Fingerprint

Cite this