Dynamics of a coupled mechanical system containing a spherical pendulum and a fractional damper

Jan Freundlich , Danuta Sado


The presented work deals with nonlinear dynamics of a three degree of freedom system with a spherical pendulum and a damper of the fractional type. Vibrations in the vicinity of the internal and external resonance are considered. The system consists of a block suspended from a linear spring and a fractional damper, and a spherical pendulum suspended from the block. The viscoelastic properties of the damper are described using the Caputo fractional derivative. The fractional derivative of an order of 0 < α≤ 1 is assumed. The impact of a fractional order derivative on the system with a spherical pendulum is studied. Time histories, the internal and external resonance, bifurcation diagrams, Poincaré maps and the Lyapunov exponents have been calculated for various orders of a fractional derivative. Chaotic motion has been found for some system parameters.
Author Jan Freundlich (FACME / IMDF)
Jan Freundlich,,
- Institute of Machine Design Fundamentals
, Danuta Sado (FACME / IMDF)
Danuta Sado,,
- Institute of Machine Design Fundamentals
Journal seriesMeccanica, ISSN 0025-6455, e-ISSN 1572-9648
Issue year2020
Publication size in sheets0.6
ASJC Classification2210 Mechanical Engineering; 2211 Mechanics of Materials; 3104 Condensed Matter Physics
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 06-09-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.201; WoS Impact Factor: 2018 = 2.316 (2) - 2018=2.208 (5)
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