Linear vibrations of continuum with fractional derivatives
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
Boundary Value Problems 2013, 2013:104 doi:10.1186/1687-2770-2013-104Published: 25 April 2013
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.