Nonlinear dynamics of a rotordynamic nonsmooth shape memory alloy system

Silva, Leandro C.; Savi, Marcelo A.; Paiva, Alberto

doi:10.1016/j.jsv.2012.09.018

Cited by 27 publications

(11 citation statements)

References 35 publications

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“…When condition a 1 a 2 > a 3 degenerates to a 1 a 2 � a 3 , a pair of pure imaginary roots appear in the solution of characteristic polynomial (8) indicating that Hopf bifurcation occurs.…”

Section: Bifurcation Analysis Of Two Subsystemsmentioning

confidence: 99%

“…e Filippov-type (piecewise smooth) systems are characterized by discontinuous vector fields and continuous Jacobian matrices. e introduction of nonsmooth terms will result in a series of special dynamic behaviors near the interface, such as sliding, traversing, grazing, and jumping [6][7][8][9]. Due to the discontinuity of the vector field, the traditional attractor analysis method [10] employed to deal with smooth systems cannot be directly used to study the special dynamic behaviors occurring in nonsmooth region.…”

Section: Introductionmentioning

confidence: 99%

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Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems

2019

Shock and Vibration

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The main purpose of this paper is to investigate the mechanism of sliding phenomenon in Filippov (nonsmooth) dynamical systems by attractor analysis and vector analysis. A corresponding simple model based on Chua’s circuit with periodic excitation was introduced as an example. The attractor analysis proposed in our previous work is used to discuss the complicated oscillations of the Filippov system. However, it failed to perfectly explain the sliding phenomena and establish an analytical method of constant voltage control. Therefore, the geometric structure and analytic conditions of sliding bifurcations in the general n-dimensional piecewise smooth system are discussed in detail by vector structure analysis. The prospects of practical application of this method are also discussed in the end.

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Section: Bifurcation Analysis Of Two Subsystemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems

2019

Shock and Vibration

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“…In the nonlinear dynamics context, oscillators with mechanical coupling have recently attracted a significant attention due to the complexity of the dynamics for high degreeof-freedom devices and possible applications to advanced technologies [16,17,18,19,20]. Among the class of mechanical coupling oscillators an interesting example is the massspring-pendulum system [21,22].…”

Section: Introductionmentioning

confidence: 99%

Characterization in bi-parameter space of a non-ideal oscillator

Souza

Batista

Baptista

et al. 2017

Physica A: Statistical Mechanics and its Applications

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We investigate the dynamical behavior of a non-ideal Duffing oscillator, a system composed of a mass-spring-pendulum driven by a DC motor with limited power supply. To identify new features on Duffing oscillator parameter space due to the limited power supply, we provide an extensive numerical characterization in the bi-parameter space by using Lyapunov exponents. Following this procedure, we identify remarkable new periodic windows, the ones known as Arnold tongues and also shrimp-shaped structures. Such windows appear in highly organized distribution with typical self-similar structures for the shrimps, and, surprisingly, codimension-2 bifurcation as a point of accumulations for the tongues.

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“…Basically, vibro-impact systems mainly fall into two categories: the impact oscillator with fixed impact body, e.g. [22,23] and the impact oscillator with one-side drifting impact body e.g. [24,25,26].…”

Section: Introductionmentioning

confidence: 99%

Forward and backward motion control of a vibro-impact capsule system

Liu

Pavlovskaia

Wiercigroch

et al. 2015

International Journal of Non-Linear Mechanics

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A capsule system driven by a harmonic force applied to its inner mass is considered in this study. Four various friction models are employed to describe motion of the capsule in different environments taking into account Coulomb friction, viscous damping, Stribeck effect, pre-sliding, and frictional memory. The non-linear dynamics analysis has been conducted to identify the optimal amplitude and frequency of the applied force in order to achieve the motion in the required direction and to maximize its speed. In addition, a position feedback control method suitable for dealing with chaos control and coexisting attractors is applied for enhancing the desirable forward and backward capsule motion.The evolution of basins of attraction under control gain variation is presented and it isshown that the basin of the desired attractors could be significantly enlarged by slight adjustment of the control gain improving the probability of reaching such an attractor.

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Nonlinear dynamics of a rotordynamic nonsmooth shape memory alloy system

Cited by 27 publications

References 35 publications

Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems

Attractor and Vector Structure Analyses of Bursting Oscillation with Sliding Bifurcation in Filippov Systems

Characterization in bi-parameter space of a non-ideal oscillator

Forward and backward motion control of a vibro-impact capsule system

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