Prediction of solutions of the Duffing system with tuned mass damper

• Autorzy: Mnich K.
• Języki publikacji: EN

Abstrakty

EN

In this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffng oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

Słowa kluczowe

EN

Duffing oscillator; tuned mass absorber; coexistence of attractors; bifurcation analysis; attractors detection; basin stability

PL

oscylator Duffinga; strojony tłumik masowy; współistnienie atraktorów; analiza bifurkacyjna; wykrywanie atraktora; stabilność basenu

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 4
• Strony: 983--989
• Opis fizyczny: Bibliogr. 10 poz., 1 rys., wykr.

Twórcy

autor

Mnich K.

• Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland

Bibliografia

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• [4] Brzeski, P., Perlikowski, P., Yanchuk, S. and Kapitaniak, T.: The dynamics of the pendulum suspended on the forced Duffng oscillator, Journal of Sound and Vibration, 331(24), 5347-5357, 2012.
• [5] Chudzik, A., Perlikowski, P., Stefanski, A. and Kapitaniak, T.: Multistability and rare attractors in van der Pol-Duffng oscillator, International Journal of Bifurcation and Chaos, 21(07), 1907-1912, 2011.
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• [8] Menck, P.J., Heitzig, J., Marwan, N. and Kurths, J.: How basin stability complements the linear-stability paradigm, Nature Physics, 9(2), 89, 2013.
• [9] Ozbudak, E.M., Thattai, M., Lim, H-M., Shraiman, B.I. and Van Oudenaarden, A.: Multistability in the lactose utilization network of escherichia coli, Nature, 427(6976), 737, 2004.
• [10] Szemplinska-Stupnicka, W., Tyrkiel, E. and Zubrzycki, A.: The global bifurcations that lead to transient tumbling chaos in a parametrically driven pendulum, International Journal of Bifurcation and Chaos, 10(09), 2161-2175, 2000.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).