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Transient growth rates of near-grazing impact velocities: Theory and experiments
University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, Illinois, USA. (Department of Mechanical Science and Engineering)
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Vehicle Dynamics. (Vehicle Dynamics)
University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, Illinois, USA. (Department of Mechanical Science and Engineering)
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Vehicle Dynamics. (Vehicle Dynamics)ORCID iD: 0000-0002-1426-1936
2009 (English)In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 325, no 4-5, 950-958 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, nonsmooth fold bifurcations associated with the onset of low-relative- velocity (near-grazing) impacts in an oscillatory mechanical system are proposed as a potential operating principle for high-speed limit switches. Specifically, analytical, numerical, and experimental methods are employed to investigate the near-grazing transient behavior in a representative system. It is shown that the rate of growth of successive impact velocities increases beyond all bounds as the threshold parameter value is approached. A limit switch based on the proposed nonsmooth fold scenario would thus be expected to outperform one that relies on a smooth bifurcation, such as the cyclic-fold bifurcation, in terms of switching speed and sensitivity.

Place, publisher, year, edition, pages
London: Academic Press , 2009. Vol. 325, no 4-5, 950-958 p.
Keyword [en]
nonlinear dynamics, non-smooth dynamics, impacts
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-11069DOI: 10.1016/j.jsv.2009.04.012ISI: 000268515900019Scopus ID: 2-s2.0-67649506227OAI: oai:DiVA.org:kth-11069DiVA: diva2:235372
Note

QC 20100811

Available from: 2009-09-15 Created: 2009-09-15 Last updated: 2017-12-13Bibliographically approved
In thesis
1. On the stability and control of piecewise-smooth dynamical systems with impacts and friction
Open this publication in new window or tab >>On the stability and control of piecewise-smooth dynamical systems with impacts and friction
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the analysis of dynamical systems suitable to be modelled by piecewise-smooth differential equations. In such systems the continuous-in-time dynamics is interrupted by discrete-in-time jumps in the state or governing equations of motion. Not only can this framework be used to describe existing systems with strong nonlinear behaviour such as impacts and friction, but the non-smooth properties can be exploited to design new mechanical devices. As suggested in this work it opens up the possibility of, for example, fast limit switches and energy transfer mechanisms.

Particularly, the dynamics at the onset of low-velocity impacts in systems with recurrent dynamics, so called grazing bifurcations in impact-oscillators, are investigated. As previous work has shown, low-velocity impacts is a strong source of instability to the dynamics, and efforts to control the behaviour is of importance. This problem is approached in two ways in this work. One is to investigate the influence of parameter variations on the dynamic behaviour of the system. The other is to implement low-cost control strategies to regulate the dynamics at the grazing bifurcation. The control inputs are of impulsive nature, and utilizes the natural dynamics of the system to the greatest extent.

The scientific contributions of this work is collected in five appended papers. The first paper consists of an experimental verification of a map that captures the correction to the smooth dynamics induced by an impact, known in the literature as the discontinuity map. It is shown that the lowest order expansion of the map accurately captures the transient growth rate of impact velocities. The second paper presents a constructive proof of a control algorithm for a rather large class of impact oscillators. The proof is constructive in the sense that it gives control parameters which stabilizes the dynamics at the onset of low-velocity impacts. In the third paper a piecewise-smooth quarter-car model is derived, and the control strategy is implemented to reduce impact velocities in the suspension system. In the fourth and fifth papers the grazing bifurcation of an impact oscillator with dry friction type damping is investigated. It turns out that the bifurcation is triggered by the disappearance of an interval of stable stick solutions. A condition on the parameters of the system is derived which differentiates between stable and unstable types of bifurcation scenarios. Additionally, a low-cost control strategy is proposed, similar to the one previously mentioned, to regulate the bifurcation scenario.

Place, publisher, year, edition, pages
Stockholm: KTH, 2009. viii, 53 p.
Series
Trita-AVE, ISSN 1651-7660 ; 2009:66
Keyword
non-smooth dynamics, nonlinear control, low-velocity impacts, friction, bifurcations
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-11079 (URN)978-91-7415-437-5 (ISBN)
Public defence
2009-10-09, D2, Lindstedtsvägen 5, Kungliga Tekniska Högskolan, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20100811Available from: 2009-09-21 Created: 2009-09-15 Last updated: 2010-08-11Bibliographically approved

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Jerrelind, Jenny

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