Fly-wheel model exhibits the hither and thither motion of a bouncing ball

Bibó, András; Károlyi, György; Bódai, Tamás

doi:10.1016/j.ijnonlinmec.2009.06.006

Cited by 12 publications

(8 citation statements)

References 36 publications

(80 reference statements)

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“…[13][14][15][16]). For such a problem, Ismail & Stronge [17] recently developed a viscoplastic model for the dissipation of energy between colliding bodies and compared it favourably with experimental data for various different sports balls.…”

Section: (A) Experimental Methodologymentioning

confidence: 99%

“…As a clue to why these discrepancies between theory and experiment may arise, it is interesting to note that even a problem as simple as the impact of a single sports ball on a hard surface is highly non-trivial (e.g. [13][14][15][16]). For such a problem, Ismail & Stronge [17] recently developed a viscoplastic model for the dissipation of energy between colliding bodies and compared it favourably with experimental data for various different sports balls.…”

Section: (B) Previous Studiesmentioning

confidence: 99%

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The two-ball bounce problem

2015

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A popular classroom demonstration is revisited in which a light ball and a much larger heavier ball are vertically aligned and dropped together onto a hard surface. Careful experimental data obtained using a high-speed camera is compared to a lumped-mass Newtonian restitution model. Good macroscopic agreement is found, provided there is sufficient separation between the two balls as they are dropped. An alternative continuum model based on elastic membrane theory is developed to explain the limit in which the balls are initially touching. The model assumes the lower ball deforms to a truncated sphere upon its impact with the floor, exciting an elastic wave which subsequently launches the upper ball like a particle on a trampoline, before the lower ball leaves the ground. A favourable comparison with experimental data is found for the case of negligible initial separation between the balls.

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Section: (A) Experimental Methodologymentioning

confidence: 99%

Section: (B) Previous Studiesmentioning

confidence: 99%

The two-ball bounce problem

2015

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“…Along with the development of engineering applications and the in-depth study of nonsmooth dynamics, impact vibration dynamics have been widely used in mechanical systems. Relevant research results have revealed the basic dynamic characteristics of various mechanical vibration systems and broadened the knowledge of the nonsmooth characteristics of such systems, such as the three-axle locomotive bogie system [30,31], ground moling [32], the fly-wheel model of a bouncing ball [33], ultrasonic percussive drilling [34], vibroimpact capsule systems [35], pressure relief valves [36], Jeffcott rotors with bearing clearance [37], impact dampers [38], and gear drives [39].…”

Section: Introductionmentioning

confidence: 99%

Diversity and Regularity of Periodic Impact Motions of a Mechanical Vibration System with Multiple Rigid Stops

Yin

Luo

Wang

2021

Shock and Vibration

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The mechanical model of a two-degree-of-freedom vibration system with multiple rigid stops was established, and the effects of the multiple rigid stops to dynamic characteristics of two mass blocks of the system were studied. The judgment conditions and differential equations of motion of the system masses impacting rigid stops were analyzed. Based on the multiparameter and multiobjective collaborative simulation analysis, the correlation between the dynamic characteristics of the vibration system and the model parameters is studied. The basic periodic and subharmonic impact motions are analyzed with emphasis on the influences of dynamical parameters on the mode diversity and the distribution characteristics, and the law of emergence and competition of various periodic impact motions on the parametric plane is revealed. The singular points, the hysteresis transition domains, and the accompanying codimension-two bifurcations, caused by the irreversibility of the transition between adjacent basic periodic impact motions in the low-frequency domain, are analyzed. The reasonable parameter matching range, associated with dynamic characteristic optimization of the system, is determined.

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“…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%

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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Fly-wheel model exhibits the hither and thither motion of a bouncing ball

Cited by 12 publications

References 36 publications

The two-ball bounce problem

The two-ball bounce problem

Diversity and Regularity of Periodic Impact Motions of a Mechanical Vibration System with Multiple Rigid Stops

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

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