Discontinuous Dynamical Systems on Time-varying Domains

Luo, Albert C. J.

doi:10.1007/978-3-642-00253-3

Cited by 80 publications

(45 citation statements)

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“…A deeper understanding of some common characters of soft impact problems can be achieved by consulting Refs. [37,38]. For the simplicity of discussion and summarization, the dynamic analysis can be considered in a dimensionless formin the following work, we assume all parameters and variables are dimensionless, which are given by…”

Section: Mechanical Modelmentioning

confidence: 99%

“…Specifically, the non-smooth force becomes increasingly evident for the soft stop with the prestressed spring so that the vector field is non-smooth on the impacting surface irrespective of the impacting velocity. Luo systematically investigated the natures of discontinuous dynamical systems on timevarying domains, which were detailedly demonstrated in recent two monographs [37,38], where some common characters associated with soft impact problems are analytically studied and concluded. The chatteringimpact vibration denotes an accumulation of impact events in finite time (or a motion period), and the sticking is where the dynamics becomes finally constrained to the impact surface as the impact attenuation stops.…”

Section: Introductionmentioning

confidence: 99%

“…One of the two oscillators connected to an excitation system intermittently impacts with an obstacle fixed on the thick steel wall associated with different gap sizes. Along with the requirement of engineering application and the increasing thorough of basic research on nonsmooth dynamics, vibro-impact dynamics has been applied to a wide range of practical mechanical systems for finding the correlative relationship between dynamic performance and model parameters, such as wheel-rail impacts of railway coaches [56,57], vibrating hammer [58], pile driver [59,60], ground moling dynamics [61], fly-wheel model of the bouncing ball [62], link mechanism [63], ultrasonic percussive drilling [64,65], vibro-impact capsule system [66], pressure relief valve [48], Jeffcott rotors with bearing clearance [67][68][69], impact dampers [70,71], excited pendula with impacts [72], vibro-impact drilling [73], gears [36][37][38][74][75][76][77]. The dynamical models designed in Refs.…”

Section: Introductionmentioning

confidence: 99%

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Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

et al. 2014

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A two-degree-of-freedom periodically forced system with a clearance is considered. The correlative relationship and matching law between dynamics and system parameters are analyzed by the co-simulation analysis of multi-parameter and multiperformance. Key parameters of the system, such as the exciting frequency, clearance value and constraint stiffness, are emphasized to analyze the influence of the main factors on its soft impact characteristics and reveal diversity, evolution and distribution regions of periodic-impact motions. The quantity of the fundamental group of p/1 impact motions, which have the excitation period and differ by the number p of impacts, is basically determined by the constraint stiffness. A series of grazing bifurcations occur with decreasing the exciting frequency so that the number p of impacts of the fundamental group of motions correspondingly increases one by one. As the constraint stiffness is very large, the impact number p of the fundamental group of motions becomes also big enough in low exciting frequency range. Consequently, the system possibly exhibits chattering-impact characteristics and the relative impact velocities successively attenuate in an excitation period. There exist a series of singular points between any two adjacent ones of the fundamental group of motions as the damping ratio or the damping constant of the viscous dashpot connecting two masses is very small, i.e., real-grazing and baregrazing bifurcation boundaries of one of them, saddlenode and period-doubling bifurcation boundaries of the other mutually cross themselves at the point of intersection and create two types of transition regions: hysteresis and tongue-shaped regions. A series of zones of regular and complex subharmonic impact motions are found to dominate in the tongue-shaped regions. The dimensionless parameters have been designed technically, under which large mass ratio or small supporting stiffness ratio leads to diversity and complexity of periodic-impact motions of the system. Based on the sampling ranges of parameters, the influence of system parameters on relative impact velocities, existence regions and correlative distribution of different types of periodic-impact motions of the system is emphatically studied.

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Section: Mechanical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

et al. 2014

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“…To study singularity in discontinuous dynamical systems, the G-functions for such systems were introduced in Luo [23], the flow switchability to the separation boundary, the switching bifurcations between non-passable and passable flows were investigated using such G-functions. Furthermore Luo [24] presented the flow switchability theory of discontinuous dynamical systems on time-varying domains, and applied such theory to different practical problems, such as the sliding motion and grazing motions in a periodically forced discontinuous dynamical system with incline line boundary, the grazing motion and stick motions for a periodically traveling belt with dry friction, the dynamics of gear transmission systems. In recent years several kinds of vibro-impact systems have been well studied by above G-functions and flow switching theory for discontinuous dynamical system.…”

Section: Introductionmentioning

confidence: 99%

Stick motions and grazing flows in an inclined impact oscillator

Zhang

2015

Chaos, Solitons & Fractals

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“…Thus, the HBM may not be an adequate method for periodic motions in such a modified rotor with discontinuity. The theory of discontinuous dynamical systems should be used from Luo [11,12]. In this paper, the buckled nonlinear Jeffcott rotor will be described through a continuous dynamical system rather than a discontinuous dynamical system.…”

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confidence: 99%

Analytical solutions of period-1 motions in a buckled, nonlinear Jeffcott rotor system

Huang

Luo

2015

Int. J. Dynam. Control

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In this paper, the analytical solutions of period-1 motions of a buckled nonlinear Jeffcott rotor are developed, and the corresponding stability and bifurcation of period-1 motion are also analyzed by eigenvalue analysis. The Hopf bifurcations of period-1 motions cause not only the bifurcation tree but quasi-periodic motions. The quasi-periodic motion can be stable or unstable. Displacement orbits of periodic motions in the buckled nonlinear Jeffcott rotor systems are illustrated, and harmonic amplitude spectrums are presented for harmonic effects on periodic motions of the buckled nonlinear Jeffcott rotor.

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Discontinuous Dynamical Systems on Time-varying Domains

Cited by 80 publications

References 0 publications

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

Stick motions and grazing flows in an inclined impact oscillator

Analytical solutions of period-1 motions in a buckled, nonlinear Jeffcott rotor system

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