Impact adding bifurcation in an autonomous hybrid dynamical model of church bell

Brzeski, P.; Chong, Antonio S.E.; Wiercigroch, Marian; Perlikowski, Przemysław

doi:10.1016/j.ymssp.2017.11.025

Cited by 24 publications

(20 citation statements)

References 23 publications

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“…The cart is connected to the support (7) with the springs (3). A stepper motor (9) is mounted on the cart with a disk (10) and an unbalance (5) in order to realize harmonic forcing. Impacts are realized by limiters of motion in the form of stops (6) mounted on the support and the cart.…”

Section: Experimental Stand and Mathematical Modelmentioning

confidence: 99%

“…It is worth noting that the obstacle grazing at frequencies from the interval ω ∈ [14; 18] does not cause the trajectory bifurcation as opposed to the phenomena at ω ∈ [20.5; 23]. Let us construct the phase portraits of typical orbits forming the so-called impact-adding scenario (do not confuse with the grazing-induced impact-adding bifurcation [10]) presented in Fig. 2d.…”

Section: The System Behavior At Low Frequenciesmentioning

confidence: 99%

“…Incorporation of dry friction and impact rheologic elements into vibration systems allows one to describe a wider range of physical processes. Corresponding mathematical models are governed by the nonsmooth equations of motions [5,[8][9][10]. The detailed analytical treatment is admitted mainly by piecewise linear models.…”

Section: Introductionmentioning

confidence: 99%

“…The attractors inherent in the smooth models can be endowed by new properties. Moreover, such models can demonstrate special types of evolution including border-collision bifurcations [10,[15][16][17][18] and chattering phenomena [19].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bifurcation phenomena and statistical regularities in dynamics of forced impacting oscillator

Skurativskyi¹,

Kudra

Witkowski

et al. 2019

Nonlinear Dyn

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The paper is devoted to the study of harmonically forced impacting oscillator. The physical model for oscillator is a cart on a guide connected to the support with springs and excited by the stepper motor. The support also is provided with limiter of motion. The mathematical model for this system is defined with the second-order piecewise smooth differential equation. Model's nonlinearity is connected with the incorporation of dry friction and generalized Hertz contact law. Analyzing the classical Poincare sections and inter-impact sequences obtained experimentally and numerically, the bifurcations and statistical properties of periodic, multiperiodic, and chaotic regimes were examined. The development of impact-adding regime as a new nonlinear phenomenon when the forcing frequency varies was observed.

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Section: Experimental Stand and Mathematical Modelmentioning

confidence: 99%

Section: The System Behavior At Low Frequenciesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bifurcation phenomena and statistical regularities in dynamics of forced impacting oscillator

Skurativskyi¹,

Kudra

Witkowski

et al. 2019

Nonlinear Dyn

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“…On the other hand, hybrid dynamical systems (HDSs) have been studied intensively by many researchers [5][6][7]. An HDS combines a continuous-time dynamical system and a discrete-time dynamical system, e.g., a circuit including a switch like a DC/DC converter [8], a neuron model including a firing scheme like the Izhikevich neuron model [9], or a conflict system like a bell [10]. HDSs embody a rich variety of bifurcation phenomena reflecting their interrupting properties and the discontinuity of their derivatives, and many bifurcation analysis tools and applications have been developed for them.…”

Section: Introductionmentioning

confidence: 99%

Influence of Bifurcation Structures Revealed by Refinement of a Nonlinear Conductance in JosephsonJunction Element

Miino

Ueta

2018

Complexity

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We conduct a bifurcation analysis of a single-junction superconducting quantum interferometer with an external flux. We approximate the current-voltage characteristics of the conductance in the equivalent circuit of the JJ by using two types of functions: a linear function and a piecewise linear (PWL) function. We describe a method to compute the local stability of the solution orbit and to solve the bifurcation problem. As a result, we reveal the bifurcation structure of the systems in a two-dimensional parameter plane. By making a comparison between the linear and PWL cases, we find a difference in the shapes of their bifurcation sets in the two-dimensional parameter plane even though there are no differences in the one-dimensional bifurcation diagrams or the trajectories. As for the influence of piecewise linearization, we discovered that grazing bifurcations terminate the calculation of the local bifurcations, because they drastically change the stability of the periodic orbit.

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Suppression of grazing-induced instability in single degree-of-freedom impact oscillators

Yin

Wen

2018

Appl. Math. Mech.-Engl. Ed.

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Impact adding bifurcation in an autonomous hybrid dynamical model of church bell

Cited by 24 publications

References 23 publications

Bifurcation phenomena and statistical regularities in dynamics of forced impacting oscillator

Bifurcation phenomena and statistical regularities in dynamics of forced impacting oscillator

Influence of Bifurcation Structures Revealed by Refinement of a Nonlinear Conductance in JosephsonJunction Element

Suppression of grazing-induced instability in single degree-of-freedom impact oscillators

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