Influence of fractional order parameter on the dynamics of different vibrating systems
Ładowanie...
Data
2021
Autorzy
Tytuł czasopisma
ISSN czasopisma
Tytuł tomu
Wydawca
Lodz University of Technology Press
Lodz University of Technology. Faculty of Mechanical Engineering. Department of Automation, Biomechanics and Mechatronics.
Wydawnictwo Politechniki Łódzkiej
Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.
Lodz University of Technology. Faculty of Mechanical Engineering. Department of Automation, Biomechanics and Mechatronics.
Wydawnictwo Politechniki Łódzkiej
Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.
Abstrakt
In this work, we will investigate the fractional differential equations associated to different
vibration phenomena. More specifically, we will discuss Bagley-Torvik equation, composite
fractional relaxation differential equation and the motion of a linear oscillator using fractional
derivative operator in the sense of Atangana-Baleanu. In order to be consistent with the physical
systems the value of the fractional parameter that characterizes the existence of fractional structures in
the system, lies within unit interval. The solutions of the non-integer order differential equation are
obtained and expressed in terms of generalized functions depending upon the fractional parameter.
The classical cases could be recovered by making the limit of fractional parameter approaches to
unity. Moreover, we will analyze and compare the control of the fractional order parameter on the
dynamics of the models and useful conclusions are recorded.
Opis
Słowa kluczowe
fractional derivative operator, vibrating systems, linear oscillators, operator różniczkowania ułamkowego, układy wibracyjne, oscylatory liniowe
Cytowanie
Zafar A.A., Awrejcewicz J., Influence of fractional order parameter on the dynamics of different vibrating systems. W: DSTA-2021 Conference Books – Abstracts (16th International Conference : Dynamical Systems Theory and Applications DSTA 2021 ABSTRACTS), Awrejcewicz J. (red.), Kaźmierczak M. (red.), Olejnik P. (red.), Mrozowski J. (red.), Wydawnictwo Politechniki Łódzkiej ; Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki, Łódź 2021, s. 64-65, ISBN 978-83-66741-20-1.