ARTICLE
Transient vibration of a fractional viscoelastic cantilever beam with an eccentric mass element at the end
1
Warsaw Univerity of Thechnology, Warsaw, Poland
Submission date: 2023-12-18
Final revision date: 2024-03-08
Acceptance date: 2024-03-20
Online publication date: 2024-04-25
Publication date: 2024-04-30
Corresponding author
Jan Freundlich
Faculty of Automotive and Construction Machinery Egineering, Warswaw University of Technology, Narbutta 84, 02-524, Warszawa, Poland
Faculty of Automotive and Construction Machinery Egineering, Warswaw University of Technology, Narbutta 84, 02-524, Warszawa, Poland
Journal of Theoretical and Applied Mechanics 2024;62(2):421-434
KEYWORDS
TOPICS
ABSTRACT
The work focuses on the transient forced vibration of a cantilever beam with a rigid eccentric
mass element attached at the free end. The Euler-Bernoulli beam theory and the viscoelastic
fractional Kelvin-Voigt material model are adopted. The equation of motion of the beam is
derived using Hamilton’s principle. The first eigenfunction of linear vibrations is used as an
approximate solution for the nonlinear vibrations. The equations of motion of the system
are solved numerically. The impact of the order of the fractional derivative on the beam
transient linear and nonlinear vibrations is studied.
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