2024 Grazing bifurcations in impact oscillators

Grazing bifurcations in impact oscillators

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WebModels of impact oscillators using an instantaneous impact law are by their very nature discontinuous. These discontinuities geve rise to bifurcations which cannot be classified … WebGrazing bifurcations in impact oscillators Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Dec;50 (6):4427-4444. doi: 10.1103/physreve.50.4427. Authors W Chin , E Ott , HE Nusse , C Grebogi PMID: 9962524 DOI: 10.1103/physreve.50.4427

Analytical Determination of Bifurcations in an Impact …

WebGuo studied the existence and bifurcations of periodic motions in a discontinuous dynamical ... When the relative phase space trajectories of two vibrators are tangent to the impact boundary, the grazing bifurcation occurs. ... D. Impacting chatter and stick in a transmission system with two oscillators. J. Multi-Body Dyn. 2009, 223, 159–188 ... WebNov 15, 2012 · A two-parameter bifurcation analysis is performed on a mathematical model that represents the motion of a pressure relief valve connected to a reservoir via a pipe and it is found that there are two independent forms of Hopf b ifurcation: a so-called valve-only instability and a coupled acoustic resonance. 13 PDF View 2 excerpts, cites background great lakes financing cleveland ohio

Grazing bifurcations and chatter in a pressure relief valve model

WebIn this paper, we propose a novel strategy for the synthesis and the classification of nonsmooth limit cycles and its bifurcations (named Non-Standard Bifurcations or Discontinuity Induced Bifurcations or DIBs) in n-dimensional piecewise-smooth dynamical systems, particularly Continuous PWS and Discontinuous PWS (or Filippov-type PWS) … WebDec 22, 2024 · Following the previous work on the degenerate grazing bifurcations of impact oscillators, this paper aims to explore novel two-parameter dynamics near the degenerate grazing points using GPU parallel computing technology. By using the technology, a further understanding of the near-grazing dynamics can be developed for … WebApr 8, 2024 · This paper investigates differences between the grazing-induced bifurcations in impact oscillators with one-sided elastic and rigid constraints by a path-following (continuation) method. great lakes financing llc

Analytical Determination of Bifurcations in an Impact …

Feedback Control of Grazing-Induced Chaos in the Single …

WebAug 25, 2009 · Normal Form Maps for Grazing Bifurcations in n-Dimensional Piecewise-Smooth Dynamical Systems,” Physica D. 0167-2789, 160 (3–4 ... Bifurcations Caused by Grazing Incidence in Many Degrees of Freedom Impact Oscillators,” Proc. R. Soc. London, Ser. A. 1364-5021, 453, pp. WebApr 13, 2024 · Simpson and R. Kuske, “ The influence of localized randomness on regular grazing bifurcations with applications to impacting dynamics,” J. Vib. Control 24, 407 ... “ The closed-form stationary probability distribution of the stochastically excited vibro-impact oscillators,” J. Sound Vib. great lakes finishing solutionsWebMay 9, 2005 · These systems exhibit complex dynamics because of inherent nonlinearities due to impacts, friction, and electric forces. As a result, dramatic changes in system behavior, associated with so-called grazing bifurcations, may occur during the transition between impacting and nonimpacting dynamics, including the presence of robust chaos. great lakes finishing

"WebDec 1, 1994 · Impact oscillators demonstrate interesting dynamical features. In particular, new types of bifurcations take place as such systems evolve from a nonimpacting to an … " - Grazing bifurcations in impact oscillators

Grazing bifurcations in impact oscillators

WebThe simplest grazing bifurcations involve orbits of period-1, but we show that the same analytical methods can be used to locate some subharmonics and their bifurcations. 1. Introduction ... In these mechanical engineering examples of impact oscillators, the primary problems caused by the successive impacts are noise and wear. Another rich WebIn this paper, the concept of discontinuity geometry of rigid impact oscillators is extended to soft impact oscillators and the mechanisms of grazing bifurcations of an impact...

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WebJun 1, 1999 · Grazing boundaries and bifurcations In the absence of friction and impact, a linear oscillator responds to harmonic forcing with a phase trajectory that carves an … WebNov 1, 2024 · Grazing bifurcations are typical non-smooth bifurcations that occur in impact oscillators. They are described by a discrete map with square-root singularities. In this paper we study the structure of… 8 Normal form maps for grazing bifurcations in n -dimensional piecewise-smooth dynamical systems M. Bernardo, C. Budd, A. Champneys …

WebJun 1, 2024 · Grazing bifurcations of the impact oscillators subjected to harmonic force can be induced by grazing contacts between the trajectory of oscillators and rigid constraints. When such events happen, abrupt changes of the system responses, i.e. creation of chaos or jump phenomena, can be observed. WebJan 1, 2024 · To control the discontinuous grazing bifurcations in impact oscillators, a new control strategy by using the degeneration of both eigenvalues and grazing bifurcations was proposed in [29]. In all of those works, the higher order terms of the normal form map of the discontinuity mapping are omitted due to computational complexity.

WebImpact oscillators demonstrate interesting dynamical features. In particular, new types of bifurcations take place as such systems evolve from a nonimpacting to an impacting … WebImpact oscillators demonstrate interesting dynamical features. In particular, new types of bifurcations take place as such systems evolve from a nonimpacting to an impacting …

WebMar 8, 2016 · The period motion maps and grazing bifurcations for soft and rigid impact oscillators have been investigated by many researchers including, respectively Luo (2005), Luo & Chen (2005) and Banerjee et al., who discovered a narrow band of chaos close to the grazing condition for a simple soft impact oscillator and showed that this abrupt onset to ...

Web× Close. The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. great lakes financial brighton miWebAnalytical and experimental investigations on bifurcation scenarios for an impact oscillator with a one-sided elastic constraint near grazing were presented by Ing et al. [45], [46]. Dynamics near grazing is thought to be governed by a complex interplay between smooth and non-smooth bifurcations. great lakes financing llc clevelandWebJul 1, 2024 · Abstract and Figures This paper presents the analysis of the degenerate grazing bifurcation in a three-degree-of-freedom impact oscillator by studying the bifurcations of near-grazing... great lakes financial spring lake miWebNov 15, 2012 · Grazing bifurcations and chattering The system (2.3) can be written in the form (3.6) x = F ( x, μ) if H ( x) > 0 together with the reset map (impact law) (3.7) x ↦ R ( x) if H ( x) = 0, in which x ∈ R n ( n = 3 for this example, but to be general we give a description that is valid for arbitrary dimensional systems). great lakes financingWebJul 1, 2024 · Abstract and Figures This paper presents the analysis of the degenerate grazing bifurcation in a three-degree-of-freedom impact oscillator by studying the … great lakes financial llcWebDec 2, 2024 · (9) and the direct numerical observations in terms of modeling and stability analysis for the degenerate grazing bifurcation case, the single degree-of-freedom impacting oscillator under harmonic excitation is taken as the example. The schematic model can be found in Fig. 1. great lakes financial group troy mi floating work schedule