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A novel approach for vibration analysis of fractional viscoelastic beams with attached masses and base excitation

Stepa Paunović, Milan Cajić, Danilo Karličić, Marina Mijalković, Danilo Karlicic Orcid Logo

Journal of Sound and Vibration, Volume: 463, Start page: 114955

Swansea University Author: Danilo Karlicic Orcid Logo

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....

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Published in: Journal of Sound and Vibration
ISSN: 0022-460X
Published: 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa52355
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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: Galerkin method, Fractional viscoelasticity, Beam mass system, Base excitation, Impulse response
College: College of Engineering
Start Page: 114955