Vibrations of a simply supported beam with a fractional viscoelastic material model – supports movement excitation

Issue title: Nonlinear vibrations in elastic structures: Dynamics and control

Article type: Research Article

Authors: Freundlich, Jan

Affiliations: Faculty of Automotive and Construction Machinery Engineering, Warsaw University of Technology, Narbutta 84, 02-524 Warsaw, Poland. Tel.: +48 22 2348459; Fax: +48 22 2348286; E-mail: jfr@simr.pw.edu.pl

Abstract: The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann – Liouville fractional derivative of order 0 α ⩽ 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann – Liouville fractional derivative with lower terminal at −∞ is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are obtained for various values of fractional derivative of order α and values of the Voigt material model parameters. The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.

Keywords: Fractional viscoelasticity, beam vibration, damping of vibrations

DOI: 10.3233/SAV-130825

Journal: Shock and Vibration, vol. 20, no. 6, pp. 1103-1112, 2013