Controlling grazing-induced multistability in a piecewise-smooth impacting system via the time-delayed feedback control

Zhang, Zhi; Chávez, Joseph Páez; Sieber, Jan; Liu, Yang

doi:10.1007/s11071-021-06511-2

Cited by 20 publications

(7 citation statements)

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“…Typical approaches employed to mitigate these failures include nanomaterial constructing, thin film coating, topographical and chemical modification [248,249]. Perhaps more important, the contact force along the tapping region can drastically increase when PD motion occurs, which may greatly influence the reliability of vibro-impact switches [14,76,250].…”

Section: Discussionmentioning

confidence: 99%

Micromechanical vibro-impact systems: a review

Tsai

2023

J. Micromech. Microeng.

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Spurred by the invention of the tapping-mode atomic force microscopy three decades ago, various micromechanical structures and systems that utilize parts with mechanical impact have been proposed and developed since then. While sharing most of the dynamical characteristics with macroscopic vibro-impact systems and benefiting from extensive theories developed, microscale counterparts possess higher percentage of surface force, higher resonance frequency and Q, and more prominent material and structural nonlinearities, all of which lead to unique features and in turn useful applications not seen in macroscopic vibro-impact systems. This paper will first present the basics of vibro-impact systems and techniques used for analyzing their nonlinear behaviors and then review the contact force modeling with an emphasis in microscale and numerical analysis tools. Finally, various applications of microscale vibro-impact systems will be reviewed and discussed. This review aims to provide a comprehensive picture of MEMS vibro-impact systems and inspire more innovative applications that take full advantage of the beauty of nonlinear vibro-impact dynamics in the microscale.

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Section: Discussionmentioning

confidence: 99%

Micromechanical vibro-impact systems: a review

Tsai

2023

J. Micromech. Microeng.

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“…Other solutions methods for nonlinear systems with piecewise functions include Harmonic Balance Method [27][28][29], coordinate transformations [30][31][32], and path-following continuation methods [1,2,33]. For the last category, authors generally resort to Numerical Continuation toolboxes, like MatCont [34], COCO [35] and AUTO-07 [36].…”

Section: Introductionmentioning

confidence: 99%

“…Liu et al [38] studied the effect of a position feedback control strategy of a vibro-impact drilling via multisegments continuation: they adopted the hspo COCO toolbox to perform their analyses. In other works [33,[39][40][41][42], authors resorted to numerical continuation toolboxes, proving their effectiveness in solving non-smooth dynamical systems. Nonetheless, the analyses available in the literature are generally limited to one or few simple orbits.…”

Section: Introductionmentioning

confidence: 99%

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

2023

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In the industry field, the increasingly stringent requirements of lightweight structures are exposing the ultimately nonlinear nature of mechanical systems. This is extremely true for systems with moving parts and loose fixtures which show piecewise stiffness behaviours. Nevertheless, the numerical solution of systems with ideal piecewise mathematical characteristics is associated with time-consuming procedures and a high computational burden. Smoothing functions can conveniently simplify the mathematical form of such systems, but little research has been carried out to evaluate their effect on the mechanical response of multi-degree-of-freedom systems. To investigate this problem, a slightly damped mechanical two-degree-of-freedom system with soft piecewise constraints is studied via numerical continuation and numerical integration procedures. Sigmoid functions are adopted to approximate the constraints, and the effect of such approximation is explored by comparing the results of the approximate system with the ones of the ideal piecewise counter-part. The numerical results show that the sigmoid functions can correctly catch the very complex dynamics of the proposed system when both the above-mentioned techniques are adopted. Moreover, a reduction in the computational burden, as well as an increase in numerical robustness, is observed in the approximate case.

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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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Controlling grazing-induced multistability in a piecewise-smooth impacting system via the time-delayed feedback control

Cited by 20 publications

References 50 publications

Micromechanical vibro-impact systems: a review

Micromechanical vibro-impact systems: a review

Approximating piecewise nonlinearities in dynamic systems with sigmoid functions: advantages and limitations

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

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