Chaotic Vibration of Fractional Calculus Model Viscoelastic Arch

Nonlinear dynamic behaviors of the fractional calculus model viscoelastic arch are discussed in this paper. The motion equations governing dynamic behaviors of the viscoelastic arch is derived and simplified by Galerkin method. The numerical method for solving the motion equations with fractional calculus is presented here. The influences of the load parameter and the material parameter are considered respectively. The results show that the chaotic vibration of the arch appears in forced vibration. And both the load parameter and the material parameter affect the dynamic behavior of the arch. With the increasing of the load parameter, the motion states changed from periodic motion with period 1 to complex motions, such as mult-periodicity, quasi-periodicity or chaos. The increasing of the material parameter benefits the stability of the structures.