Nonlinear dynamic characteristics of a vibro-impact system under harmonic excitation

Jian, Cheng; Xu, Haibo

doi:10.2140/jomms.2006.1.239

Cited by 6 publications

(2 citation statements)

References 28 publications

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“…The investigations of stability in systems with impacts, periodic motions, bifurcations, singularities at vibroimpact dynamics were noted in this review. The works devoted to learning of discontinuous dynamical systems [4][5][6][7][8][9][10][11][12][13][14][15][16] were discussed shortly.…”

Section: Introductionmentioning

confidence: 99%

Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Баженов

Pogorelova

Postnikova

2016

Applied Mathematics and Nonlinear Sciences

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Dynamic behaviour of contact impact forces in strongly nonlinear discontinuous vibroimpact system is studying. Contact impact force is one of the most significant vibroimpact system characteristics. We investigate the 2-DOF vibroimpact system by numerical parameter continuation method in conjunction with shooting and Newton-Raphson methods. We simulate the impact by nonlinear contact interactive force according to Hertz’s contact law. This paper is the continuation of the previous works [1,2]. We have determined the instability zones and bifurcations points for loading curves [1] and frequency-amplitude response [2] under variation of excitation amplitude and frequency. In this paper we investigate the behaviour of contact forces at bifurcation points particularly at discontinuous bifurcation points where set-valued Floquet multipliers cross the unit circle by jump that is their moduli becoming more than unit by jump. It is phenomenon unique for nonsmooth systems with discontinuous right-hand side. We observe also the contact forces increase at nT -periodical multiple impacts regimes. We also learn the change of contact forces behaviour when the impact between system bodies became the soft one due the change of system parameters.

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Section: Introductionmentioning

confidence: 99%

Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Баженов

Pogorelova

Postnikova

2016

Applied Mathematics and Nonlinear Sciences

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“…Non-smooth dynamical system is a special category of nonlinear system. In practice, it is not difficult to find non-smooth dynamical systems, such as a hammer hitting a nail, a signal triggering an electrical circuit, and a disaster affecting the stock market [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Dynamics Analysis for Periodically Forced Oscillation System

Lü

Mao

2010

AMR

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Among various non-smooth dynamic systems, the periodically forced oscillation system with impact is the most common in engineering applications. The dynamics becomes complicate due to the impact against the stops. This paper presented a systematic study on the periodically forced oscillation system with impact. In particular, impulsive differential equation, Poincare map is applied. The proposed model has high numerical accuracy in describing their dynamics. It helps to optimize the design of a commercial product.

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