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Autoparametric Vibrations of a Nonlinear System with a Pendulum and Magnetorheological Damping

  • Jerzy Warminski
  • Krzysztof Kecik
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 181)

Abstract

The chapter deals with autoparametric vibrations of a system composed of a nonlinear oscillator with an attached pendulum. Dynamics of the mechanical structure is studied analytically around the principal parametric resonance region, numerically and experimentally for a wide range of parameters. The influence of damping, nonlinear stiffness (hard and soft), amplitude and frequency of excitation on the system’s behaviour is analysed in details. The obtained results show that the pendulum can be applied as a dynamical absorber. However, for selected parameters, near the main parametric resonance, instability, which transits the pendulum to chaotic oscillations or to a full rotation, occurs. Therefore, the application of a magnetorheological (MR) damper and a nonlinear spring is proposed to improve the dynamics and to control the response online. Periodic vibrations, chaotic motions or a full rotation of the pendulum obtained numerically are confirmed by the experiment. The chaotic nature of motion is determined from real signals by the attractor reconstruction and the recurrence plot calculation. The results show that the semi-active suspension may reduce dangerous motion and it also allows to maintain the pendulum at a given attractor or to jump to another one.

Keywords

Autoparametric vibrations control stability chaos parametric resonance magnetorheological damping nonlinearity basins of attraction 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jerzy Warminski
    • 1
  • Krzysztof Kecik
    • 1
  1. 1.Department of Applied MechanicsLublin University of TechnologyLublinPoland

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