Application of fractional calculus in the dynamics of beams
1 Department of Mathematics, Faculty of Art & Science, Celal Bayar University, Manisa, 45047, Turkey
2 Department of Civil Engineering, Faculty of Engineering, Celal Bayar University, Manisa, 45140, Turkey
Boundary Value Problems 2012, 2012:135 doi:10.1186/1687-2770-2012-135Published: 15 November 2012
This paper deals with a viscoelastic beam obeying a fractional differentiation constitutive law. The governing equation is derived from the viscoelastic material model. The equation of motion is solved by using the method of multiple scales. Additionally, principal parametric resonances are investigated in detail. The stability boundaries are also analytically determined from the solvability condition. It is concluded that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations.