Applied nonlinear dynamics of non-smooth mechanical systems

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

This paper introduces practically important concept of local non-smoothness where any dynamical system can be considered as smooth in a finite size subspace of global hyperspaceO. Global solution is generated by matching local solutions obtained by standard methods. If the dynamical system is linear in all subspaces then an implicit global analytical solution can be given, as the times when non-smoothness occurs have to be determined first. This leads to the necessity of solving a set of nonlinear algebraic equations. To illustrate the non-smooth dynamical systems and the methodology of solving them, three mechanical engineering problems have been studied. Firstly the vibro-impact system in a form of moling device was modelled and analysed to widerstand how the progression rates can be maximised. Periodic trajectories can be reconstructed as they go through three linear subspaces (no contact, contact with progression and contact without progression). In the second application fractional chatter occurring during metal cutting has been examined via numerical simulation method. The analysis has shown that the bifurcation analysis can be very useful to make an appropriate choice of the system parameters to avoid chatter. The last problem comes from rotordynamics, where nonlinear interaction between the rotor and the snubber ring are studied. The results obtained from the developed mathematical model confronted with the experiment have shown a good degree of correlation.
Original languageEnglish
Pages (from-to)519-526
Number of pages8
JournalJournal of the Brazilian Society of Mechanical Sciences and Engineering
Volume28
Issue number4
Publication statusPublished - 1 Oct 2006

Fingerprint

Dynamical systems
Metal cutting
Mechanical engineering
Nonlinear equations
Rotors
Trajectories
Mathematical models
Computer simulation
Experiments

Cite this

Applied nonlinear dynamics of non-smooth mechanical systems. / Wiercigroch, M.

In: Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 28, No. 4, 01.10.2006, p. 519-526.

Research output: Contribution to journalArticle

@article{e56694364ef5434a9f4b0cd219a9a348,
title = "Applied nonlinear dynamics of non-smooth mechanical systems",
abstract = "This paper introduces practically important concept of local non-smoothness where any dynamical system can be considered as smooth in a finite size subspace of global hyperspaceO. Global solution is generated by matching local solutions obtained by standard methods. If the dynamical system is linear in all subspaces then an implicit global analytical solution can be given, as the times when non-smoothness occurs have to be determined first. This leads to the necessity of solving a set of nonlinear algebraic equations. To illustrate the non-smooth dynamical systems and the methodology of solving them, three mechanical engineering problems have been studied. Firstly the vibro-impact system in a form of moling device was modelled and analysed to widerstand how the progression rates can be maximised. Periodic trajectories can be reconstructed as they go through three linear subspaces (no contact, contact with progression and contact without progression). In the second application fractional chatter occurring during metal cutting has been examined via numerical simulation method. The analysis has shown that the bifurcation analysis can be very useful to make an appropriate choice of the system parameters to avoid chatter. The last problem comes from rotordynamics, where nonlinear interaction between the rotor and the snubber ring are studied. The results obtained from the developed mathematical model confronted with the experiment have shown a good degree of correlation.",
author = "M. Wiercigroch",
note = "Copyright 2008 Elsevier B.V., All rights reserved.",
year = "2006",
month = "10",
day = "1",
language = "English",
volume = "28",
pages = "519--526",
journal = "Journal of the Brazilian Society of Mechanical Sciences and Engineering",
issn = "1678-5878",
publisher = "Brazilian Society of Mechanical Sciences and Engineering",
number = "4",

}

TY - JOUR

T1 - Applied nonlinear dynamics of non-smooth mechanical systems

AU - Wiercigroch, M.

N1 - Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2006/10/1

Y1 - 2006/10/1

N2 - This paper introduces practically important concept of local non-smoothness where any dynamical system can be considered as smooth in a finite size subspace of global hyperspaceO. Global solution is generated by matching local solutions obtained by standard methods. If the dynamical system is linear in all subspaces then an implicit global analytical solution can be given, as the times when non-smoothness occurs have to be determined first. This leads to the necessity of solving a set of nonlinear algebraic equations. To illustrate the non-smooth dynamical systems and the methodology of solving them, three mechanical engineering problems have been studied. Firstly the vibro-impact system in a form of moling device was modelled and analysed to widerstand how the progression rates can be maximised. Periodic trajectories can be reconstructed as they go through three linear subspaces (no contact, contact with progression and contact without progression). In the second application fractional chatter occurring during metal cutting has been examined via numerical simulation method. The analysis has shown that the bifurcation analysis can be very useful to make an appropriate choice of the system parameters to avoid chatter. The last problem comes from rotordynamics, where nonlinear interaction between the rotor and the snubber ring are studied. The results obtained from the developed mathematical model confronted with the experiment have shown a good degree of correlation.

AB - This paper introduces practically important concept of local non-smoothness where any dynamical system can be considered as smooth in a finite size subspace of global hyperspaceO. Global solution is generated by matching local solutions obtained by standard methods. If the dynamical system is linear in all subspaces then an implicit global analytical solution can be given, as the times when non-smoothness occurs have to be determined first. This leads to the necessity of solving a set of nonlinear algebraic equations. To illustrate the non-smooth dynamical systems and the methodology of solving them, three mechanical engineering problems have been studied. Firstly the vibro-impact system in a form of moling device was modelled and analysed to widerstand how the progression rates can be maximised. Periodic trajectories can be reconstructed as they go through three linear subspaces (no contact, contact with progression and contact without progression). In the second application fractional chatter occurring during metal cutting has been examined via numerical simulation method. The analysis has shown that the bifurcation analysis can be very useful to make an appropriate choice of the system parameters to avoid chatter. The last problem comes from rotordynamics, where nonlinear interaction between the rotor and the snubber ring are studied. The results obtained from the developed mathematical model confronted with the experiment have shown a good degree of correlation.

UR - http://www.scopus.com/inward/record.url?scp=33847755105&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33847755105

VL - 28

SP - 519

EP - 526

JO - Journal of the Brazilian Society of Mechanical Sciences and Engineering

JF - Journal of the Brazilian Society of Mechanical Sciences and Engineering

SN - 1678-5878

IS - 4

ER -