Wei ZHANG
The Journal of Mechanical Science and Technology, vol. 23, no. 4, pp.1058-1064, 2009

Abstract : The nonlinear dynamic behaviors of oscillators described by fractional-order differential are presented in this paper. The background of the research is based upon two engineering practices. First is that the visco-elastic behaviors of some advanced polymeric materials can be accurately modeled by the fractional calculus constitutive law. Second is that the influence of nonlinear visco-elasticity described by the fractional operator cannot be neglected in some cases such as the vibration with large displacement or large strain and thermo-visco-elastic coupled problems. The numerical scheme for solving the nonlinear equation of motion is developed. The results show that because of the introduction of nonlinear damping modeled by the fractional-order operator, the bifurcation and chaos of the oscillator appear in forced vibration. Furthermore, the fraction value of the fractional operator evidently affects the dynamic behavior of the nonlinear fractional differential oscillator.

Keyword : Nonlinearity; Fractional calculus; Bifurcation; Chaos; Viscoelasticity