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Nonlinear dynamics of dry friction oscillator subjected to combined harmonic and random excitations

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Abstract

The dynamics of a nonlinear single degree freedom oscillator on a moving belt subjected to combined harmonic and random excitations is numerically investigated. The dynamics is described by differential equations with discontinuities due to dry friction between the mass and the belt. The discontinuous oscillator is modelled as a Filippov system. Discontinuity induced bifurcations such as the adding sliding bifurcations due to harmonic excitation and stochastic bifurcations like the P and D bifurcations are investigated by numerically integrating the equations of motion using an adaptive time stepping method. A bisection approach is used to accurately determine the discontinuity point, and a Brownian tree approach is used to follow the correct Brownian path. The associated Fokker–Planck (FP) equation is solved by the finite element method. The largest Lyapunov exponent is computed by using the Müller jump matrix and the Wedig algorithm. The effects of the system parameters on the dynamics of the system are investigated.

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Data Availability

The dataset in Sect. 6 was generated using Matlab scripts. The Matlab codes developed for this work are available from the corresponding author on reasonable request.

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Acknowledgements

This is to acknowledge that this work was originally presented online in the 16th International conference of Dynamical Systems-Theory and Applications (DSTA-2021), 6–9 December 2021 and was recommended by the DSTA committee for publication in post-DSTA issue of Journal of Nonlinear Dynamics.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Dynamic Analysis Group, Bharat Heavy Electricals Limited, Nagpur, 440001, India

    Pankaj Kumar

  2. IIITDM, Kancheepuram, India

    S. Narayanan

  3. Indian Institute of Technology Madras, Chennai, 600036, India

    S. Narayanan

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  1. Pankaj Kumar
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Correspondence to S. Narayanan.

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Kumar, P., Narayanan, S. Nonlinear dynamics of dry friction oscillator subjected to combined harmonic and random excitations. Nonlinear Dyn 109, 755–778 (2022). https://doi.org/10.1007/s11071-022-07483-7

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