Authors: Paunović, Stepa 
Cajić, Milan 
Karličić, Danilo 
Mijalković, Marina
Title: A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation
Journal: Journal of Sound and Vibration
Volume: 463
Issue Date: 22-Dec-2019
Rank: M21
ISSN: 0022-460X
DOI: 10.1016/j.jsv.2019.114955
Abstract: 
The Galerkin method is widely applied for finding approximate solutions to vibration problems of beam and plate structures and for estimating their dynamic behavior. Most studies employ the Galerkin method in the analysis of the undamped systems, or for simple structure models with viscous damping. In this paper, a novel approach of using the Galerkin method and Fourier transform to find the solution to the problem of vibration of fractionally damped beams with an arbitrary number of attached concentrated masses and base excitation is presented. The considered approach is novel and it lends itself to determination of the impulse response of the beam and leads to the solution of the system of coupled fractional order differential equations. The proposed approximate solution is validated against the exact solution for a special case with only one tip mass attached, as well as against the Finite Element Method Solution for a special case with classical viscous damping model. Numerical analysis is also given, including the examples of vibration analysis of viscoelastic beams with different fractional derivative orders, retardation times, and the number, weight and position of the attached masses.
Keywords: Base excitation | Beam mass system | Fractional viscoelasticity | Galerkin method | Impulse response
Publisher: Elsevier
Project: Dynamics of hybrid systems with complex structures. Mechanics of materials. 
Marie Skłodowska-Curie Actions - European Commission fellowship, 799201-METACTIVE

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