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Nonlinear analysis of a shimmying wheel with contact-force characteristics featuring higher-order discontinuities

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Abstract

In this study, the yaw dynamics of a towed caster wheel system is analysed via an in-plane, one degree-of-freedom mechanical model. The force and aligning torque generated by the elastic tyre are calculated by means of a semi-stationary tyre model, in which the piecewise-smooth characteristic of the tyre forces is also considered, resulting in a dynamical system with higher-order discontinuities. The focus of our analysis is the Hopf bifurcation affected by the non-smoothness of the system. The structure of the analysis is organised in a similar way as in case of smooth bifurcations. Firstly, the centre-manifold reduction is performed, then we compose the normal form of the bifurcation. Based on the Galerkin technique an approximate, semi-analytical method to calculate the limit cycles is introduced and compared with the method of collocation. The analysis provides a deeper insight into the development of the vibrations associated with wheel shimmy and demonstrate how the non-smoothness due to contact-friction influences the dynamic behaviour.

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Acknowledgements

This research was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

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Authors and Affiliations

  1. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Sándor Beregi

  2. MTA-BME Research Group on Dynamics of Machines and Vehicles, Budapest, Hungary

    Dénes Takács

  3. Department of Hydrodynamic Systems, Budapest University of Technology and Economics, Budapest, Hungary

    Csaba Hős

Authors
  1. Sándor Beregi
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  2. Dénes Takács
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  3. Csaba Hős
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Correspondence to Sándor Beregi.

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Beregi, S., Takács, D. & Hős, C. Nonlinear analysis of a shimmying wheel with contact-force characteristics featuring higher-order discontinuities. Nonlinear Dyn 90, 877–888 (2017). https://doi.org/10.1007/s11071-017-3699-3

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  • DOI: https://doi.org/10.1007/s11071-017-3699-3

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