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Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.

Contact impact forces at discontinuous 2-DOF vibroimpact. (English) Zbl 1433.70037

Appl. Math. Nonlinear Sci. 1, No. 1, 183-196 (2016).
Summary: 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 [the authors et al., Stability and Bifurcations Analysis for 2-DOF Vibroimpact System by Parameter Continuation Method. Part I: Loading Curve. J. Appl. Nonlin. Dyn. 4, No. 4, 357–370 (2015; doi:10.5890/JAND.2015.11.003), Part 2: Frequency-Amplitude response. ibid. 5, No. 3, 269–281 (2016; doi:10.5890/JAND.2016.09.002)]. We have determined the instability zones and bifurcations points for loading curves In Part I and frequency-amplitude response in Part II 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.

Cited in 3 Documents

MSC:

70K50 Bifurcations and instability for nonlinear problems in mechanics
70K43 Quasi-periodic motions and invariant tori for nonlinear problems in mechanics
37M20 Computational methods for bifurcation problems in dynamical systems
65P30 Numerical bifurcation problems
65P40 Numerical nonlinear stabilities in dynamical systems

Keywords:

stability; vibroimpact system; discontinuous; contact force; Hertz’s law; bifurcation; multiplier; nonlinear
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References:

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