Numerical Bifurcation Analysis of Discontinuous 2-DOF Vibroimpact System. Part 2: Frequency-Amplitude Response

et al. 2018

OMTC

Chaotic behaviour of dynamical systems, their routes to chaos, and the intermittency are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in nonsmooth dynamical systems is of the special scientists' interest. In this paper we apply relatively young mathematical tool -continuous wavelet transform CWT -for investigating the chaotic behavior and intermittency in particular in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate route to chaos via intermittency, to distinguish and analyze the laminar and turbulent phases.

Section: The Initial Equationsmentioning

confidence: 99%

Wavelet transform using for analysis of vibroimpact system chaotic behavior

et al. 2018

OMTC

“…So far as this paper is the continuation of works [1,2] the problem formulation is the same. We'll repeat it shortly.…”

Section: Problem Formulation the Initial Equationsmentioning

confidence: 99%

“…Recently the investigations of such systems are developed rapidly. The short literature survey was made in [2]. The investigations of stability in systems with impacts, periodic motions, bifurcations, singularities at vibroimpact dynamics were noted in this review.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Applied Mathematics and Nonlinear Sciences

2016

Self Cite

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.

“…1). We had studied its dynamical behaviour in our previous papers [6][7][8][9]. We had seen several zones of instability when the control parameter -external loading frequency -had been varying.…”

Section: Introductionmentioning

confidence: 99%

Intermittent transition to chaos in vibroimpact system

Applied Mathematics and Nonlinear Sciences

2018

Self Cite

Chaotic behaviour of dynamical systems, their routes to chaos, and the intermittency in particular are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in non-smooth dynamical systems is of the special scientists’ interest. In this paper we study the type-III intermittency route to chaos in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We apply relatively new mathematical tool – continuous wavelet transform CWT – for investigation this phenomenon. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate intermittency route to chaos, to distinguish and analyze the laminar and turbulent phases.