Stick motions and grazing flows in an inclined impact oscillator

Fu, Xilin; Zhang, Yanyan

doi:10.1016/j.chaos.2015.04.005

Cited by 29 publications

(6 citation statements)

References 35 publications

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“…The best way to explain this behavior is with the impact-pair model, which is described as the ball of a point mass moving freely inside a 1D box and reflecting when hitting the boundary of the box. Due to the existence of the impacts, it has extremely complicated dynamical behavior, such as grazing bifurcation, singularity, and chaotic attractor [16][17][18][19]. The second is that a proper approach to studying VI systems is to attempt to establish its discrete Poincaré map (sometimes called the first return map).…”

Section: Introductionmentioning

confidence: 99%

Global Dynamics of a Vibro-Impact Energy Harvester

Cao

et al. 2022

Mathematics

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In this paper, we consider a two-sided vibro-impact energy harvester described as a forced cylindrical capsule inclined at a horizontal angle, and the motion of the ball inside the capsule follows from the impacts with the capsule ends and gravity. Two distinct cases of dynamical behavior are investigated: the nondissipative and dissipative cases, where the dissipation is given by a restitution coefficient of impacts. We show that the dynamics of the system are described by the use of a 2D implicit map written in terms of the variables’ energy and time when the ball leaves the moving capsule ends. More precisely, in the nondissipative case, we analytically show that this map is area-preserving and the existence of invariant curves for some rotation number with Markoff constant type is proved according to Moser’s twist theorem in high energy. The existence of invariant curves implies that the kinetic energy of the ball is always bounded, and hence, the structure of system is not destroyed by the impacts of the ball. Furthermore, by numerical analysis we also show that the dynamical behavior of this system is regular, mainly containing periodic points, invariant curves and Aubry–Mather sets. After introducing dissipation, the dissipation destroys the regular dynamical behavior of the nondissipative case, and a periodic point with low energy is generated.

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Section: Introductionmentioning

confidence: 99%

Global Dynamics of a Vibro-Impact Energy Harvester

Cao

et al. 2022

Mathematics

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“…In the same year, Sun and Fu [66] studied the discontinuous dynamical behaviors of a SDOF oscillator. Based on this general theory, many investigations on this kind of system with friction and impact have been done, and specific examples can be found in [67]- [75].…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Dynamic Analysis of a Class of 2-DOF Oscillators With Strong Nonlinearity Under a Periodic Excitation

2021

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Starting from the car suspension system, the nonlinear characteristics of a class of twodegree-of-freedom oscillators with strong nonlinearity under a periodic excitation are discussed by the switching theory of flow in discontinuous dynamical systems. Based on the discontinuous forces and different motions of the two masses, the phase plane of each mass is composed of stick domain, nonstick domain (or free domain) and separation boundary in absolute and relative coordinates, respectively. The swithching criteria between the stick and nonstick motions and the conditions of grazing motion in two different regions are developed via the G-functions and switching control laws. The mapping dynamics theory is used to give the four-dimensional transformation set and four-dimensional mapping, and the conditions for periodic motions are explored. In addition, the stick motions, two kinds of grazing motions, periodic motions for this system and a comparison of the velocities, accelerations (or forces responses) of the two masses under the two conditions of control force are simulated numerically. The results show that the stability and comfort of the vehicle can be improved by adjusting the control force, which is generated by the control unit of system or exerted by the external excitation. For further investigating the influence of system parameters on dynamical behaviors, the stick and grazing bifurcation scenarios varying with driving frequency or amplitude are also developed, which can provide useful information for parameter selection of vibration systems with clearance and the optimal design of vehicle suspension systems. This paper also has important reference value for practical applications in other industries or machinery with elastic impacts.

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“…Generally, there is only small understanding for the actual instantaneous conditions that are responsible for the self-excitation in real-world braking systems. Decades of brake squeal research illustrate the fugitive character of this highly nonlinear [25], multi-scale [27] and chaotic [15,28] phenomenon. In the contribution at hand, deep learning techniques are employed to learn the functional relations between operational conditions of the dynamical structure and its vibrational response.…”

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confidence: 98%

Deep learning for brake squeal: vibration detection, characterization and prediction

Stender,

Tiedemann,

Spieler

et al. 2020

Preprint

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Despite significant advances in numerical modeling of brake squeal, the majority of industrial research and design is still conducted experimentally. In this work we report on novel strategies for handling data-intensive vibration testings and gaining better insights into brake system vibrations. To this end, we propose machine learning-based methods to detect and characterize vibrations, understand sensitivities and predict brake squeal. Our aim is to illustrate how interdisciplinary approaches can leverage the potential of data science techniques for classical mechanical engineering challenges. In the first part, a deep learning brake squeal detector is developed to identify several classes of typical sounds in vibration recordings. The detection method is rooted in recent computer vision techniques for object detection. It allows to overcome limitations of classical approaches that rely on spectral properties of the recorded vibrations. Results indicate superior detection and characterization quality when compared to state-of-the-art brake squeal detectors. In the second part, deep recurrent neural networks are employed to learn the parametric patterns that determine the dynamic stability of the brake system during operation. Given a set of multivariate loading conditions, the models learn to predict the vibrational behavior of the structure. The validated models represent virtual twins for the squeal behavior of a specific brake system. It is found that those models can predict the occurrence and onset of brake squeal with high accuracy. Hence, the deep learning models can identify the complicated patterns and temporal dependencies in the loading conditions that drive the dynamical structure into regimes of instability. Large data sets from commercial brake system testing are used to train and validate the deep learning models.

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Stick motions and grazing flows in an inclined impact oscillator

Cited by 29 publications

References 35 publications

Global Dynamics of a Vibro-Impact Energy Harvester

Global Dynamics of a Vibro-Impact Energy Harvester

Discontinuous Dynamic Analysis of a Class of 2-DOF Oscillators With Strong Nonlinearity Under a Periodic Excitation

Deep learning for brake squeal: vibration detection, characterization and prediction

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