Vibration of Functionally Graded Beam Subjected to Moving Oscillator Using Caputo-Fabrizio Fractional Derivative Model

In this paper, the vibration of an Euler-Bernoulli functionally graded beam under a moving oscillator is investigated. The beam is considered to be simply supported whereas its material composition is varying along the thickness according to a power law. Furthermore, the internal damping of the beam...

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Bibliographic Details
Published in:Romanian Journal of Acoustics and Vibration 2019-01, Vol.16 (2), p.137-146
Main Authors: Almbaidin, Amro, Abu-Alshaikh, Ibrahim
Format: Article
Language:English
Subjects:
Beams (structural)
Boundary conditions
Damping ratio
Dynamic response
Functionally gradient materials
Laplace transforms
Load
Researchers
Velocity
Vibration
Viscoelasticity
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Summary:In this paper, the vibration of an Euler-Bernoulli functionally graded beam under a moving oscillator is investigated. The beam is considered to be simply supported whereas its material composition is varying along the thickness according to a power law. Furthermore, the internal damping of the beam is modeled by viscoelastic fractional Kelvin-Voigt model which is described by Caputo-Fabrizio definition. However, the novelty in this paper is the utilizing of Caputo-Fabrizio definition which has two main advantages over other fractional derivative models; it does not contain fractional powers in the Laplace transformation domain and it is more convenient in describing material heterogeneities. The governing equations are solved by the decomposition method coupled with Laplace transforms. Three comparison studies were conducted and good agreements were obtained. The results clearly indicate the advantages of using Caputo-Fabrizio fractional derivative model. Also it is observed that the oscillator velocity, the material grading order, the damping ratio, and the fractional derivative order have significant effects on the dynamic response of the beam.
ISSN:1584-7284
2602-0351