Discontinuous dynamical behaviors in a vibro-impact system with multiple constraints

Xue, She‐Sheng; Fan, Jinjun

doi:10.1016/j.ijnonlinmec.2017.10.009

Cited by 34 publications

(4 citation statements)

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“…Other grazing-related features studied in SDOF VI systems include a dramatic increase in eigenvalues of unstable solutions near grazing, in [18], vanishing singularities of the Jacobian matrix in [21], sufficient conditions for periodic orbits that branch off of the grazing bifurcation [22], and comparisons of Nordmark and Poincaré maps to study grazing born from high-amplitude chaotic attractors [13]. In addition to the above-mentioned studies there are others, including [23][24][25][26] SDOF systems with linear dynamics between one-sided impacts, linear SDOFs with twosided impacts [27][28][29][30][31][32][33][34] and oblique impacts [35], as well as multi-DOF systems with impacts [14,15,[36][37][38][39][40]. Relevant information and references for the dynamics and bifurcations in non-smooth systems and related analytical methods can be found in books [4][5][6]41,42] and in the review paper [43].…”

Section: Introductionmentioning

confidence: 99%

Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs

2022

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A combined analysis of smooth and non-smooth bifurcations captures the interplay of different qualitative transitions in a canonical model of an impact pair, a forced capsule in which a ball moves freely between impacts on either end of the capsule. The analysis, generic for the impact pair context, is also relevant for applications. It is applied to a model of an inclined vibro-impact energy harvester device, where the energy is generated via impacts of the ball with a dielectric polymer on the capsule ends. While sequences of bifurcations have been studied extensively in single- degree-of-freedom impacting models, there are limited results for two-degree-of-freedom impacting systems such as the impact pair. Using an analytical characterization of impacting solutions and their stability based on the maps between impacts, we obtain sequences of period doubling and fold bifurcations together with grazing bifurcations, a particular focus here. Grazing occurs when a sequence of impacts on either end of the capsule are augmented by a zero-velocity impact, a transition that is fundamentally different from the smooth bifurcations that are instead characterized by eigenvalues of the local behavior. The combined analyses allow identification of bifurcations also on unstable or unphysical solutions branches, which we term ghost bifurcations. While these ghost bifurcations are not observed experimentally or via simple numerical integration of the model, nevertheless they can influence the birth or death of complex behaviors and additional grazing transitions, as confirmed by comparisons with the numerical results. The competition between the different bifurcations and their ghosts influences the parameter ranges for favorable energy output; thus, the analyses of bifurcation sequences yield important design information.

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Section: Introductionmentioning

confidence: 99%

Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs

2022

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Section: Introductionmentioning

confidence: 99%

Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs

Serdukova

Kuske

Yurchenko

2022

Preprint

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A combined analysis of smooth and non-smooth bifurcations captures the interplay of different qualitative transitions in a canonical model of an impact pair, a forced capsule in which a ball moves freely between impacts on either end of the capsule. The analysis, generic for the impact pair context, is also relevant for applications. It is applied to a model of an inclined vibro-impact energy harvester device, where the energy is generated via impacts of the ball with a dielectric polymer on the capsule ends. While sequences of bifurcations have been studied extensively in single degree of freedom impacting models, there are limited results for two degree of freedom impacting systems such as the impact pair. Using an analytical characterization of impacting solutions and their stability based on the maps between impacts, we obtain sequences of period doubling and fold bifurcations together with grazing bifurcations, a particular focus here. Grazing occurs when a sequence of impacts on either end of the capsule are augmented by a zero velocity impact, a transition that is fundamentally different from the smooth bifurcations that are instead characterized by eigenvalues of the local behavior. The combined analyses allow identification of bifurcations also on unstable or unphysical solutions branches, which we term ghost bifurcations. While these ghost bifurcations are not observed numerically or experimentally, nevertheless they can influence the birth or death of complex behaviors and additional grazing transitions, as confirmed by comparisons with numerical results. The competition between the different bifurcations and their ghosts influences the parameter ranges for favorable energy output; thus the analyses of bifurcation sequences yields important design information.PACS: 05.45.-a , 34.50.Ez

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“…[14][15][16][17][18][19][20][21] In a multi-degree-of-freedom vibro-impact system, the response behaviors were correlated and coupled, and the solution of the motion equations were more complicated. Xue and Fan 22 and Fan and Yang 23 studied the 2-degree-of-freedom vibroimpact system with multiple constraints and analyzed the periodic response of the system after establishing the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Vibration control analysis of the power head for a rotary drilling rig

Lei

Diao

2019

Advances in Mechanical Engineering

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Impacting between the multilayer Kelly bar and the power head has a detrimental effect on the drilling system and may cause huge losses to the construction engineering and machinery. This study is a further development of the vibro-impact mechanism, and especially, the study considers the constraint of the steel rope on the multilayer Kelly bar. Efficient analytical models are presented, and the total responses are obtained. Three types of displacement response are found by changing the matching relationship of global parameters. The first type has the optimal vibration control performance with the shortest path and no periodicity. The second type is inferior to the first type. The third type has the worst vibration-control performance with the longest path and periodicity. Then this article proposes the general feasibility to get the first type of displacement response and the most effective way is controlling the steel rope velocity. The research provides the foundation for the intelligent control of steel rope velocity on the rig machine.

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Discontinuous dynamical behaviors in a vibro-impact system with multiple constraints

Cited by 34 publications

References 38 publications

Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs

Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs

Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs

Vibration control analysis of the power head for a rotary drilling rig

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