Nonlinear Dynamics

, Volume 86, Issue 3, pp 1571–1597 | Cite as

Nonlinear dynamics and chaotic control of a flexible multibody system with uncertain joint clearance

  • Zhe Wang
  • Qiang Tian
  • Haiyan Hu
  • Paulo Flores
Original Paper


The nonlinear dynamics of a flexible multibody system with interval clearance size in a revolute joint is investigated in this work. The system is modeled by using a unified mesh of absolute nodal coordinate formulation (ANCF), that is, the flexible parts are meshed via the finite elements of the ANCF and the rigid parts are described via the ANCF reference nodes (ANCF-RNs). The kinetic models of all revolute joints are formulated by using ANCF reference node (ANCF-RN) coordinates. The influence of the Lund-Grenoble and the modified Coulomb’s friction models on the system dynamics is comparatively studied. The Chebyshev tensor product sampling method is used to generate the samples of the interval clearance size. With the purpose to maintain the continuous contact of the clearance joint, a modified extended delayed feedback control (EDFC) is used to stabilize the chaotic motion of the flexible multibody system. Finally, the dynamics of a planar slider–crank mechanism with interval clearance size in a revolute joint is studied, as a benchmark example, to check the effectiveness of the presented computation method and the modified EDFC.


Revolute clearance joint Slider–crank mechanism Absolute nodal coordinate formulation (ANCF) ANCF reference node (ANCF-RN) Interval parameter Extended delayed feedback control (EDFC) 



This research was supported in part by National Natural Science Foundation of China under Grants 11290151 and 11472042. The work was also supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020—Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941. Finally, the authors are much indebted to the anonymous reviewers for useful comments, recommendations and suggestions.


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Mechanical EngineeringUniversity of Minho Campus de AzuremGuimarãesPortugal

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