Novel two-parameter dynamics of impact oscillators near degenerate grazing points

Yin, Shu; Wen, Guilin; Ji, Jinchen; Xu, Huidong

doi:10.1016/j.ijnonlinmec.2020.103403

Cited by 31 publications

(12 citation statements)

References 59 publications

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“…The right-hand side given in Eq. ( 2) is a typical non-autonomous dynamical system with the one-sided elastic constraint considered as the non-smoothness that can lead to complex phenomena, such as the grazing bifurcation [34,40], the coexistence of multistable attractors [41,42] and the chaotic motions [37]. Here, we consider the situation that system (1) with u(τ ) = 0 has many coexisting attractors within some specific ranges of the system parameters.…”

Section: Single-degree-of-freedom Oscillator With Piecewise-smooth No...mentioning

confidence: 99%

Controlling coexisting attractors of a class of non-autonomous dynamical systems

Zhang,

Chávez,

Sieber

et al. 2021

Preprint

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This paper studies a control method for switching stable coexisting attractors of a class of non-autonomous dynamical systems. The central idea is to introduce a continuous path for the system's trajectory to transition from its original undesired stable attractor to a desired one by varying one of the system parameters according to the information of the desired attractor. The behaviour of the control is studied numerically for both non-smooth and smooth dynamical systems, using a soft-impact and a Duffing oscillators as examples. Special attention is given to identify the regions where the proposed control strategy is applicable by using path-following methods implemented via the continuation platform COCO. It is shown that the proposed control concept can be implemented through either using an external control input or varying a system parameter. Finally, extensive numerical results are presented to validate the proposed control methods.

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Section: Single-degree-of-freedom Oscillator With Piecewise-smooth No...mentioning

confidence: 99%

Controlling coexisting attractors of a class of non-autonomous dynamical systems

Zhang,

Chávez,

Sieber

et al. 2021

Preprint

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“…When an attractor encounters a grazing event, it may change qualitatively (see, e.g. [18][19][20]), which is called a discontinuity-induced (or, short, discontinuous or non-smooth) bifurcation. Nordmark [21] and Pavlovskaia et al [22] analyse what dynamics occurs near grazing events.…”

Section: Introductionmentioning

confidence: 99%

Controlling grazing-induced multistability in a piecewise-smooth impacting system via the time-delayed feedback control

et al. 2021

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Grazing events may create coexisting attractors and cause complex dynamics in piecewise-smooth dynamical systems. This paper studies the control of grazing-induced multistability in a soft impacting oscillator by using the time-delayed feedback control. The control switches from one of the coexisting attractors to a desired one to suppress complex dynamics near grazing events. We use path-following (continuation) techniques for non-smooth dynamical systems to investigate robustness of the controller and the parameter dependence of the controlled system. In particular, several newly developed computational methods are used, including a numerical method for analysing non-smooth delay equations and a method for calculating the Lyapunov exponents and the grazing point estimation. Numerical simulations demonstrate that the delayed feedback controller is effective, and a proper selection of the control gain and delay time can simplify the complex dynamics of the system near grazing.

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“…As a special bifurcation of nonsmooth systems, the grazing bifurcation is a qualitative transition between impact and nonimpact motion [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Nordmark [31,32] studied the dynamic behavior near the grazing trajectory and a nonlinear mapping is obtained.…”

Section: Introductionmentioning

confidence: 99%

“…e existence condition and stability of the grazing periodic orbit are derived in a two degree-of-freedom vibroimpact system with one-sided constraint in [36]. Yin et al [37][38][39][40][41][42] analyzed and measured the degenerate grazing bifurcations of the impact systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Behaviors of a Two‐Degree‐of‐Freedom Impact Oscillator with Two‐Sided Constraints

Meng

2021

Shock and Vibration

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The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the single constraint system presented in the literature to the two-sided elastic constraint system discussed in this paper. The Poincare mapping of double grazing periodic motion is derived, and this compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. According to the deduced theoretical result, the grazing curve and the codimension-two grazing bifurcation points are validated by numerical simulation. Finally, various types of periodic-impact motions near the codimension-two grazing bifurcation point are illustrated through the unfolding diagram and phase diagrams.

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Novel two-parameter dynamics of impact oscillators near degenerate grazing points

Cited by 31 publications

References 59 publications

Controlling coexisting attractors of a class of non-autonomous dynamical systems

Controlling coexisting attractors of a class of non-autonomous dynamical systems

Controlling grazing-induced multistability in a piecewise-smooth impacting system via the time-delayed feedback control

Dynamic Behaviors of a Two‐Degree‐of‐Freedom Impact Oscillator with Two‐Sided Constraints

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