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Melnikov-based criterion to obtain the critical velocity in axially moving viscoelastic strings under a set of non-Gaussian parametric bounded noise

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Abstract

Using an analytic approach, the critical velocity of chaos for an axially moving viscoelastic string under a noisy axial tension was studied in this paper. A Wiener process non-Gaussian bonded noise was selected to model the noisy fluctuations of axial force, and the Melnikov-based criterion was chosen to obtain the boundaries of chaotic behavior and consequently the critical velocity. The latter was obtained in terms of the amplitude, frequency and bandwidth of the noise. The effect of variation of the elastic and the viscous properties of the string on the qualitative and quantitative behaviors was also investigated. It was observed that the unstable area and the critical velocity depend completely on the bandwidth of the noise. Also, to ensure the correctness of the method, some of the results were validated using the corresponding Poincaré maps.

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  1. Hydro-Aeronautical Research Center, Shiraz University, 71348-51154, Shiraz, Iran

    Alireza Asnafi

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Correspondence to Alireza Asnafi.

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Asnafi, A. Melnikov-based criterion to obtain the critical velocity in axially moving viscoelastic strings under a set of non-Gaussian parametric bounded noise. Acta Mech 232, 3495–3508 (2021). https://doi.org/10.1007/s00707-021-03004-6

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  • DOI: https://doi.org/10.1007/s00707-021-03004-6

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