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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

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

Journal of Applied Nonlinear Dynamics 5(3) (2016) 269--281 | DOI:10.5890/JAND.2016.09.002

V.A. Bazhenov; P.P. Lizunov; O.S. Pogorelova; T.G. Postnikova

Kyiv National University of Construction and Architecture, 31, Povitroflotskiy avenu, Kyiv, Ukraine

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Abstract

This paper discusses bifurcations in nonlinear vibroimpact system. It is a discontinuous dynamical system. We were studying stability and bifurcations in specific two-body two-degree-of-freedom vibroimpact system by numerical parameter continuation method. We adapted parameter continuation technique for this system. Theoretical basis for dynamic characteristics composition was presented in [1]. The instability zones and bifurcation points for loading curves were determined in [1] under excitation amplitude variation. In this paper we investigate the instability zones and bifurcation points under variation of excitation frequency when we consider the frequency-amplitude response. We have observed phenomena unique for nonsmooth systems with discontinuous right-hand side: discontinuous bifurcation points where set-valued Floquet multipliers cross the unit circle by jump. At these points monodromy matrix is changed by jump too. We also have observed chattering regimes leading to chaos.

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