Post-grazing dynamics of a vibro-impacting energy generator

Serdukova, Larissa; Kuske, Rachel; Yurchenko, Daniil

doi:10.1016/j.jsv.2020.115811

Cited by 21 publications

(15 citation statements)

References 53 publications

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“…Non-dimensionalization of ( 1) and ( 2) with (3) allows us to streamline the analysis, by reducing the number of parameters to some key dimensionless quantities. Furthermore, we introduce a relative position Z (t) in terms of the difference of the non-dimensional displacements of the cylinder X * and of the ball x * as in [58,59],…”

Section: The Vi-eh Modelmentioning

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: The Vi-eh Modelmentioning

confidence: 99%

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

2022

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“…Soft impacts occur in mechanical systems when an object hits an obstacle with a negligible mass but with a non-negligible stiffness, see e.g. [35][36][37][38][39]. As can be seen from Fig.…”

Section: Single-degree-of-freedom Oscillator With Piecewise-smooth No...mentioning

confidence: 99%

Controlling coexisting attractors of a class of non-autonomous dynamical systems

Zhang,

Chávez,

Sieber

et al. 2021

Preprint

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This paper studies a control method for switching stable coexisting attractors of a class of non-autonomous dynamical systems. The central idea is to introduce a continuous path for the system's trajectory to transition from its original undesired stable attractor to a desired one by varying one of the system parameters according to the information of the desired attractor. The behaviour of the control is studied numerically for both non-smooth and smooth dynamical systems, using a soft-impact and a Duffing oscillators as examples. Special attention is given to identify the regions where the proposed control strategy is applicable by using path-following methods implemented via the continuation platform COCO. It is shown that the proposed control concept can be implemented through either using an external control input or varying a system parameter. Finally, extensive numerical results are presented to validate the proposed control methods.

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“…Through the study of actual mechanical engineering problems, it is found that the treatment of non-smooth systems under noise disturbance is often a big hassle [1][2][3]. Different types of mechanical systems, such as hydraulic safety valves, aircraft wings, energy harvesting, flexible manipulator with clearance, rotor-stator interactions in turbines and so on, will inevitably produce non-smooth dynamics [4][5][6][7][8][9][10][11]. The vibro-impact systems are one of the most widely used groups of non-smooth systems which can be simplified into the discontinuous systems represented by the process before and after the impact.…”

Section: Introductionmentioning

confidence: 99%

A Novel Method for Solving Response of Stochastic Vibro-impact Systems with Two-sided Barriers

Ma¹,

Ning

Wang

et al. 2022

Preprint

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The research of stochastic steady-state response of vibration systems including bilateral impacts and gaps has important theoretical and practical significance. At present, conventional analytical methods destroy the inherent non-smooth of the systems because of many approximate transformations when solving response. In order to deal with this problem, we propose a new method to preserve the velocity jump under the bilateral impact without nonsmooth transformation in this paper. A complete process is regarded as the one-step transition probability that the stochastic trajectories start from one barrier, and return to the original barrier after impacting with another barrier. Then, the intervals of response are established based on the initial barrier to ensure of the continuity of the state space. We analyzed the steady-state response of a bilateral Rayleigh vibro-impact oscillator and a piezoelectric energy harvesting device with two symmetric barriers by utilizing the proposed method, respectively. Comparing with Monte Carlo simulations, it is fully demonstrated the effectiveness of this method. At the same time, it is found that the cases using our proposed method have wide applicability under different position of barriers, restitution coefficient, noise excitation and system parameters.

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Post-grazing dynamics of a vibro-impacting energy generator

Cited by 21 publications

References 53 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

Controlling coexisting attractors of a class of non-autonomous dynamical systems

A Novel Method for Solving Response of Stochastic Vibro-impact Systems with Two-sided Barriers

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