Stability and Bifurcations Analysis for 2-DOF Vibroimpact System by Parameter Continuation Method. Part I: Loading Curve

Баженов, В. Г.; Lizunov, Petro; Pogorelova, O. S.; Postnikova, Tetiana; Отрашевская, Валентина Владимировна

doi:10.5890/jand.2015.11.003

Cited by 18 publications

(6 citation statements)

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“…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%

“…Numerical analysis of dynamic behaviour of contact impact forces was fulfilled by parameter continuation method in conjunction with shooting and Newton-Raphson methods [1]. Periodic motion stability or instability is determined by matrix monodromy eigenvalues that is by Floquet multipliers' values.…”

Section: Numerical Analysismentioning

confidence: 99%

“…We have described the theoretical basis for analysis of two-body two-degree-of-freedom system in [1]. Numerical system parameters are given further in Table 6.…”

Section: Numerical Analysismentioning

confidence: 99%

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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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“…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%

Section: Numerical Analysismentioning

confidence: 99%

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Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Баженов

Pogorelova

Postnikova

2016

Applied Mathematics and Nonlinear Sciences

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“…Bazhenov et al studied the strongly nonlinear, nonsmooth, and discontinuous dynamic process of a 2-degree of freedom (DOF) two-body vibration system. Amplitude-frequency 2 of 15 response parameters were obtained by controlling the external loading frequency parameter [8][9][10]. Akkerman [11] used smoothed particle hydrodynamics (SPH) to calculate the drag acting on a hull at different speeds and pitch angles, compared it with the experimental conclusions of [12].…”

Section: Introductionmentioning

confidence: 99%

Direct Sailing Variable Acceleration Dynamics Characteristics of Water-Jet Propulsion with a Screw Mixed-Flow Pump

Han

Shang

et al. 2019

Applied Sciences

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Strong nonlinearity and the relevance of time-varying dynamic parameters in the maneuverable process of water-jet propulsion were major problems encountered in the prediction of variable acceleration dynamics characteristics. The relationships between the thrust and rotation speed of a screw mixed-flow pump, drag and submerged speed of water-jet propulsion were obtained from flume experiments and numerical calculations, based on which a dynamic model of pump-jet propulsion was established in this paper. As an initial condition, the numerical solution of the submerged speed with respect to time was inputted to computational fluid dynamics (CFD) for unsteady calculation based on a user-defined function (UDF). Thus, the relationships between the acceleration, drag, net thrust, propulsion torque and efficiency with respect to time were revealed. The results indicate that the relationship between the thrust and rotational speed of a water-jet propeller is a quadratic function, which agrees well with the experimental values. The variation of submerged speed with respect to time satisfies a hyperbolic tangent function distribution. The acceleration increases sharply at the beginning and then decreases gradually to zero, especially at high rotation speeds of the water-jet pump. The variations in drag and propulsion efficiency with respect to time coincide with the step response of a second-order system with critical damping. The method and results of this study can give a better understanding of the changes in dynamic parameters such as velocity, acceleration, thrust, and drag during the acceleration of a pump-jet submersible and helped to estimate the effects of pump performance on water-jet propulsion kinetic parameters.

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“…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

Баженов

Pogorelova

Postnikova

2018

Applied Mathematics and Nonlinear Sciences

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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.

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Stability and Bifurcations Analysis for 2-DOF Vibroimpact System by Parameter Continuation Method. Part I: Loading Curve

Cited by 18 publications

References 0 publications

Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Contact Impact Forces at Discontinuous 2-DOF Vibroimpact

Direct Sailing Variable Acceleration Dynamics Characteristics of Water-Jet Propulsion with a Screw Mixed-Flow Pump

Intermittent transition to chaos in vibroimpact system

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