Bifurcation analysis of wheel shimmy with non-smooth effects and time delay in the tyre–ground contact

Sandor Beregi*, Denes Takacs, Gabor Stepan

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

38 Citations (Scopus)


The nonlinear dynamics of towed wheels is analysed with the help of the brush tyre model. The time delay in the tyre–ground contact and the non-smooth nature of the system caused by contact friction are considered simultaneously. Firstly, the centre manifold reduction is performed on the infinite-dimensional system transforming the governing equations into a normal form containing linear and piecewise-smooth second-order terms. Then, this normal form is used to establish the stability of the non-hyperbolic equilibria of the system and to give an estimation of the limit cycles emerging at the linear stability boundary. This way, it is demonstrated how subcritical Hopf bifurcations in the non-smooth delayed system generate bistable parameter ranges, which are left undetected by standard tyre models.

Original languageEnglish
Pages (from-to)841-858
Number of pages18
JournalNonlinear Dynamics
Issue number1
Publication statusPublished - 1 Oct 2019

Bibliographical note

Funding Information:
This research was funded by the National Research, Development and Innovation Office under Grant No. NKFI-128422.

Publisher Copyright:
© 2019, The Author(s).


  • Delayed tyre model
  • Non-smooth bifurcation
  • Wheel shimmy


Dive into the research topics of 'Bifurcation analysis of wheel shimmy with non-smooth effects and time delay in the tyre–ground contact'. Together they form a unique fingerprint.

Cite this