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The Effect of Dam** on the Energy Transfer in the Spherical Pendulum with Fractional Dam** in a Pivot Point

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Perspectives in Dynamical Systems II — Numerical and Analytical Approaches (DSTA 2021)

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Abstract

Nonlinear vibrations of a system with three degrees of freedom with a spherical pendulum are investigated. The system contains an oscillator and a spherical pendulum suspended from the oscillator. The dam** at the pendulum pivot point is assumed to be modelled by a fractional derivative. The viscoelastic dam** properties are described using the fractional Caputo derivative of order \(0 <\alpha \le 1\) . Vibrations in the vicinity of the internal and external resonance are considered. The effect of the order of the fractional derivative on the vibrations of the autoparametric system is studied. Responses of the system, the internal and external resonance, bifurcation diagrams, Poincaré maps and the Lyapunov exponents have been calculated for various orders of fractional derivatives. Chaotic motion has been found for some system parameters.

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Authors and Affiliations

  1. Warsaw University of Technology, Warsaw, Poland

    Jan Freundlich & Danuta Sado

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  1. Jan Freundlich
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  2. Danuta Sado
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Correspondence to Jan Freundlich .

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  1. Department of Automation, Biomechanics and Mechatronics, Łódź University of Technology, Łódź, Poland

    Jan Awrejcewicz

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Freundlich, J., Sado, D. (2024). The Effect of Dam** on the Energy Transfer in the Spherical Pendulum with Fractional Dam** in a Pivot Point. In: Awrejcewicz, J. (eds) Perspectives in Dynamical Systems II — Numerical and Analytical Approaches. DSTA 2021. Springer Proceedings in Mathematics & Statistics, vol 454. Springer, Cham. https://doi.org/10.1007/978-3-031-56496-3_14

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