Application of fractional calculus in the dynamics of beams

Boundary value problems

N Bildik¹  BG Sinir³  D Dnmez Demir³ 

[1] Science, Celal Bayar University, Manisa, Turkey;Department of Civil Engineering, Faculty of Engineering, Celal Bayar University, Manisa, Turkey;Department of Mathematics, Faculty of Art &

关键词: perturbation method;    fractional derivative;    method of multiple scales;    linear vibrations;   

DOI  :  10.1186/1687-2770-2012-135

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY