Applied nonlinear dynamics of non-smooth mechanical systems

Wiercigroch, Marian

doi:10.1590/s1678-58782006000400018

Cited by 16 publications

(3 citation statements)

References 28 publications

(33 reference statements)

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“…Applications of vibro-impact mechanical systems occur in many branches of technology such as percussive drilling, ultrasonic machining and ground moling [1]. Such systems are inherently nonlinear due to the presence of the non-smooth or discontinuous system characteristics.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a new electro-vibro-impact system

Nguyen

Woo

2010

Nonlinear Dyn

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A variety of nonlinear dynamic responses for a new electro-vibro-impact system is presented, with indication of chaotic behavior. By mathematical modeling of the physical system, an insight is obtained to the global system dynamics. The modeling has established a good correlation with experimental data, and hence can be used as a numerical tool to optimize the system dynamics. In particular, with respect to impact forces and progression rate, may then be achieved with minimal computational cost.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a new electro-vibro-impact system

Nguyen

Woo

2010

Nonlinear Dyn

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“…Although the model considers the discontinuity of the rolling element collision force, it does not consider the transient impact between the adjacent rolling elements, due to the difference in the rotational speed. Currently, the non-smooth characteristics are primarily studied for the discontinuous contact between the rotor and the cageless bearing [22,23]. Chávez et al [24] studied the non-smooth characteristics of the discontinuous contact between the rotor and the inner ring raceway due to the impact when the rotor is dropped, and established the bearing non-smooth two-degrees-of-freedom differential equations of the motion by combining the intermittent contact-induced unbalanced impact force with the rotor-bearing relative vector displacement.…”

Section: Introductionmentioning

confidence: 99%

Discrete Dynamics of Balls in Cageless Ball Bearings

2022

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Cageless ball bearings are often preferred as a back-up bearing for active magnetic bearings to support a falling rotor, but the contact between the balls of the cageless ball bearing may lead to the deterioration of the bearing performance and affect the dynamic stability of the rotor system. Thus, we studied the discrete dynamics of cageless ball bearings. First, a model is proposed to change the groove curvature center of the local outer raceway to control the ball velocity to achieve dispersion. Combined with the spatial geometry theory, the mathematical model of the discrete raceway is established, the collision between the balls is considered as an abruptly added constraint, and the non-smooth dynamics equation of the cageless ball bearing with a local discrete raceway is established. Then, the fourth-order Adams prediction correction algorithm is used to numerically solve the dynamic discretization of the ball, and the structural parameters of the discrete raceway are preferably selected, according to the phase diagram of the ball and the change in the angular spacing. The results show that the structure of the discrete raceway has a strong influence on the discrete dynamics of the ball.

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“…However from a mathematical point of view, problems with nonsmooth characteristics are not easy to handle as the resulting models are dynamical systems whose right-hand sides are discontinuous, and therefore they require a special mathematical treatment and robust numerical algorithms to produce reliable solutions. Practically, a combination of numerical, analytical and semi-analytical methods are used to survey such systems (Wiercigroch, 2006).…”

Section: Introductionmentioning

confidence: 99%

Control of a class of nonsmooth dynamical systems

Erfanian

Skandari

Kamyad

2013

Journal of Vibration and Control

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In this paper, the authors propose an approach to control a class of nonsmooth continuous and discontinuous dynamical systems which is based on a generalization of derivative and Chebyshev pseudospectral (PS) methods. First a generalized derivative for nonsmooth functions, which is proposed by Kamyad et al. is considered. Therefore the obtained generalized derivative of a nonsmooth function is approximated with the Fourier series. So, the nonsmooth control problem is approximated by a smooth optimal control problem and in what follows, it is solved by Chebyshev PS method and the approximate solution for the state and control of the main problem is achieved. Finally, some numerical examples of the control of nonsmooth dynamical systems are solved to illustrate the efficiency of the authors’ approach.

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Applied nonlinear dynamics of non-smooth mechanical systems

Abstract: This paper introduces practically important concept of local non

Cited by 16 publications

References 28 publications

Nonlinear dynamics of a new electro-vibro-impact system

Nonlinear dynamics of a new electro-vibro-impact system

Discrete Dynamics of Balls in Cageless Ball Bearings

Control of a class of nonsmooth dynamical systems

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