Open Access Research

Linear vibrations of continuum with fractional derivatives

Duygu Dönmez Demir1*, Necdet Bildik1 and Berra Gültekin Sinir2

Author Affiliations

1 Department of Mathematics, Faculty of Art & Sciences, Celal Bayar University, Manisa, 45047, Turkey

2 Department of Civil Engineering, Faculty of Engineering, Celal Bayar University, Manisa, 45140, Turkey

For all author emails, please log on.

Boundary Value Problems 2013, 2013:104  doi:10.1186/1687-2770-2013-104

Published: 25 April 2013

Abstract

In this paper, linear vibrations of axially moving systems which are modelled by a fractional derivative are considered. The approximate analytical solution is obtained by applying the method of multiple scales. Including stability analysis, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted by graphs. It is determined that the external excitation force acting on the system has an effect on the stiffness of the system. Moreover, the general algorithm developed can be applied to many problems for linear vibrations of continuum.

Keywords:
linear vibrations; dynamic analysis of continuum; fractional derivative; perturbation method