A Numerical Study of an Impact Oscillator With the Addition of Dry Friction

Cone, Kerry; Zadoks, R.I.

doi:10.1006/jsvi.1995.0617

Cited by 47 publications

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“…For a piecewise system, there exists nonconventional bifurcation, the grazing bifurcation [8]. There is much research studying the peculiar phenomena of nonsmooth dynamical systems, e.g., periodic motions to chaos via period-doubling bifurcations [9][10][11], the response going to chaos from periodic motion directly [12], the fragmentation of strange attractors [13], which are qualitatively different from the typical route to chaos in the usual consecutive maps. Impact in rotor-bearing systems is generally caused by the interactions between the rotor and bearing case.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear response and nonsmooth bifurcations of an unbalanced machine-tool spindle-bearing system

2008

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In this effort, a six-degree-of-freedom (DOF) model is presented for the study of a machinetool spindle-bearing system. The dynamics of machine-tool spindle system supported by ball bearings can be described by a set of second order nonlinear differential equations with piecewise stiffness and damping due to the bearing clearance. To investigate the effect of bearing clearance, bifurcations and routes to chaos of this nonsmooth system, numerical simulation is carried out. Numerical results show when the inner race touches the bearing ball with a low speed, grazing bifurcation occurs. The solutions of this system evolve from quasi-periodic to chaotic orbit, from period doubled orbit to periodic orbit, and from periodic orbit to quasi-periodic orbit through grazing bifurcations. In addition, the tori doubling process to chaos which usually occurs in the impact system is also observed in this spindle-bearing system.

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Section: Introductionmentioning

confidence: 99%

Nonlinear response and nonsmooth bifurcations of an unbalanced machine-tool spindle-bearing system

2008

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“…In recent years, vibro-impact problems have become a new subject in nonlinear dynamics. Subjects of recent research include singularity [Chatterjee and Mallik 1996;Whiston 1992]; inelastic vibro-impacts [Luo et al 2001]; high codimension bifurcation [Wen 2001;Luo and Xie 2003;Xie and Ding 2005]; Hopf bifurcations [Padmanabhan and Singh 1995;Luo and Chen 2005;Ding et al 2004;Luo 2004a]; and quasiperiodic impacts [BlazejczykOkolewska 2001;Luo 2004b;Cone and Zadoks 1995]; and so on. Dynamics and bifurcations of a class of single-degree-of-freedom self-excited oscillators with an impact damper were studied by Chatterjee and Mallik [1995].…”

Section: Introductionmentioning

confidence: 99%

“…Dynamics and bifurcations of a class of single-degree-of-freedom self-excited oscillators with an impact damper were studied by Chatterjee and Mallik [1995]. Cone and Zadoks [1995] investigated the nonlinear behavior of an impact oscillator with the addition of dry friction. The periodic solutions were interpreted by using bifurcation theory and the nonlinear behavior of this system was identified as a function of both the excitation amplitude and the excitation frequency for the two levels of dry friction force.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic characteristics of a vibro-impact system under harmonic excitation

Jian

2006

JOMMS

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Dynamical behaviors of a two-degree-of-freedom (TDOF) vibro-impact system are investigated. The theoretical solution of periodic-one double-impact motion is obtained by differential equations, periodicity and matching conditions, and the Poincaré map is established. The dynamics of the system are studied with special attention to Hopf bifurcations of the impact system in nonresonance, weak resonance, and strong resonance cases. The Hopf bifurcation theory of maps in ‫ޒ‬ 2 -strong resonance is applied to reveal the existence of Hopf bifurcations of the system. The theoretical analyses are verified by numerical solutions. The evolution from periodic impacts to chaos in nonresonance, weak resonance, and strong resonance cases, is obtained by numerical simulations. The results show that dynamical behavior of the system in the strong resonance case is more complicated than that of the nonresonance and weak resonance cases.

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“…Such mechanical systems have been mainly investigated in the single-degree-of-freedom or the two-degreeof-freedom case, in order to study the behaviour of the response: periodic responses [5; 9] including sticking motions [10; 11] in the undamped case and chaotic responses [12] have been found, bifurcations, transitions and global behaviours have been examined [13][14][15][16][17] including grazing bifurcations [18][19][20] and non-smooth phenomena [21][22][23]. Some authors have studied more complicated models including both impacts and friction [24][25][26], or clearance variations [27]. Some authors also considered the issue of controlling systems with impacts ( [8; 13; 28-30] etc.).…”

Section: Introductionmentioning

confidence: 99%

Comparison of several numerical methods for mechanical systems with impacts

Janin

Lamarque

2001

Numerical Meth Engineering

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International audienceThe modellization of mechanical systems with non-linearities of impact type leads to discontinuities in the velocity. In this paper, we study some numerical methods adapted to the occurrence of such discontinuities from a single-degree-of-freedom vibro-impact system. Theoretical results of consistency are given for numerical methods valid for smooth ordinary differential equations, with several kinds of procedures for approximating impact times. The algorithms are applied to classical Newmark and Runge-Kutta schemes, and the numerical behaviour is investigated for two categories of periodic response, either with finite or infinite number of impacts per cycle. These numerical methods are compared to a scheme without explicit computation of impact times. We show that high orders of convergence can be obtained with appropriate schemes, and we discuss the time of computation needed in each case

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A Numerical Study of an Impact Oscillator With the Addition of Dry Friction

Cited by 47 publications

References 0 publications

Nonlinear response and nonsmooth bifurcations of an unbalanced machine-tool spindle-bearing system

Nonlinear response and nonsmooth bifurcations of an unbalanced machine-tool spindle-bearing system

Nonlinear dynamic characteristics of a vibro-impact system under harmonic excitation

Comparison of several numerical methods for mechanical systems with impacts

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