Grazing bifurcations and chaos in the dynamics of a hydraulic damper with relief valves

D Eyres, Richar, PT Piiroinen, AR Champneys, NAJ Lieven

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Abstract

This paper numerically investigates the closed loop dynamics of a lumped mass attached to a linear spring and a nonlinear hydraulic damper with relief valves. The damper in question is designed to have piecewise linear characteristics. The inclusion of the nonlinear damper into the closed loop system leads to regions of periodic motion separated by regions of non-periodic dynamics as the forcing frequency changes. Analysis of the system uses discontinuous nonsmooth numerical continuation techniques to follow the stable and unstable solutions along with bifurcation diagrams to aid the understanding of the non-periodic dynamics. The impacting of the relief valves leads to grazing bifurcation analysis using discontinuity mappings that explains some `corners' observed in the bifurcation diagram and predicts the onset of chaotic dynamics. Other nonsmooth events such as the grazing of an invariant torus are suggested by numerical simulations.
Original languageEnglish
Publication statusUnpublished - 2004

Bibliographical note

Sponsorship: R.D. Eyres would like to acknowledge the support of CASE
award (01305192) from Westland Helicopters Ltd. and EPSRC. P.T. Piiroinen would
like to acknowledge the support of the EU FP5 Project SICONOS (IST-2001-37172).

Keywords

  • hydraulic damper
  • valves
  • grazing bifurcation
  • nonlinear

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