For flexible elements of drives characterized by a constant speed of longitudinal motion, we propose a method for the analytic investigation of vibrations caused by the action of a periodic system of impulsive perturbations. On the basis of this method, we obtain analytic relations for the description of the determining parameters of nonlinear vibrations in the analyzed class of systems for both nonresonance and resonance cases. It is shown that, in the resonance case, the value of the amplitude of transition through the resonance strongly depends on the speed of longitudinal motion of the flexible element.
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References
O. V. Kapustyan, M. O. Perestyuk and O. M. Stanzhytskyi, Extreme Problems: Theory, Examples, Methods of Solving, VPTs Kyiv Univ., Kyiv (2019).
Yu. A. Mitropols’kii, Selected Works, Naukova Dumka, Kyiv (2012).
Yu. A. Mitropols’kii and B. I. Moseenkov, Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola, Kyiv (1976).
P. I. Ogorodnikov, V. M. Svitlytskyi and V. I. Gogol, “Investigation of the relationship between longitudinal and torsional vibrations of the drill string”, Naft. Galuz’ Ukr., No. 2, 6–9 (2014).
M. O. Perestyuk and O. S. Chernikova, “Some modern aspects of the theory of impulsive differential equations”, Ukr. Mat. J., 60, No. 1, 81–94 (2008); English translation: Ukr. Math. J., 60, No. 1, 1–107 (2008); https://doi.org/10.1007/s11253-008-0044-5.
Ye. V. Kharchenko and M. B. Sokil, “Oscillations of moving nonlinearly elastic media and asymptotic methods for their investigations”, Nauk. Visn. Nats. Lisotekh. Univ. of Ukraine, 16, No. 1, 134–138 (2006).
A. Andrukhiv, M. Sokil, B. Sokil, S. Fedushko, Yu. Syerov, V. Karovic, and T. Klynina, “Influence of impulse disturbances on oscillations of nonlinearly elastic bodies”, Mathematics (MDPI), 9, No. 8, 13 p. (2021); https://doi.org/10.3390/math9080819.
L. Q. Chen, “Analysis and control of transverse vibrations of axially moving strings”, Appl. Mech. Rev., 58, No. 2, 91–116 (2005); https://doi.org/10.1115/1.1849169.
L. Q. Chen, B. Wang, and H. Ding, “Nonlinear parametric vibration of axially moving beams: asymptotic analysis and differential quadrature verification”, J. Phys.: Conf. Ser., 181, 1–8 (2009); https://doi.org/10.1088/1742-6596/181/1/012008.
L. Cveticanin and T. Pogany, “Oscillator with a sum of non-integer order non-linearities”, J. Appl. Math., 2012, 20 (2012); https://doi.org/10.1155/2012/649050.
O. Lyashuk, Y. Vovk, B. Sokil, V. Klendii, R. Ivasechko, and T. Dovbush, “Mathematical model of a dynamic process of transporting a bulk material by means of a tube scraping conveyor”, Agricultural Engineering International: CIGR Journal, 21, No. 1, 74–81 (2019).
B. I. Sokil, P. Ya. Pukach, M. B. Sokil, and M. I. Vovk, “Advanced asymptotic approaches and perturbation theory methods in the study of the mathematical model of single-frequency oscillations of a nonlinear elastic body”, Math. Model. Comput., 7, No. 2, 269–277 (2020); https://doi.org/10.23939/mmc2020.02.269.
Y. Tian, P. Yuan, F. Yang, J. Gu, M. Chen, J. Tang, Y. Su, T. Ding, K. Zhang, and Q. Cheng, “Research on the principle of a new flexible screw conveyor and its power consumption”, Applied Sci. (MDPI), 8, No. 7, 14 p. (2018); https://doi.org/10.3390/app8071038.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 64, No. 4, pp. 124–132, October–December, 2021.
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Andrukhiv, A.I., Huzyk, N.M., Sokil, B.I. et al. Dynamics of Flexible Elements of a Drive under the Action of Impulsive Perturbations. J Math Sci 279, 270–281 (2024). https://doi.org/10.1007/s10958-024-07010-6
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DOI: https://doi.org/10.1007/s10958-024-07010-6