| Affiliation: | 1.School of Mechatronic Engineering, China University of Mining and Technology,Xuzhou,P.R. China;2.Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, China University of Mining and Technology,Xuzhou,P.R. China;3.Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos,Madrid,Spain |
| Abstract: | The bifurcation and resonance phenomena are investigated in a fractional Mathieu-Duffing oscillator which contains a fast parametric excitation and a slow external excitation. We extend the method of direct partition of motions to evaluate the response for the parametrically excited system. Besides, we propose a numerical method to simulate different types of local bifurcation of the equilibria. For the nonlinear dynamical behaviors of the considered system, the linear stiffness coefficient is a key factor which influences the resonance phenomenon directly. Moreover, the fractional-order damping brings some new results that are different from the corresponding results in the ordinary Mathieu-Duffing oscillator. Especially, the resonance pattern, the resonance frequency and the resonance magnitude depend on the value of the fractional-order closely. |
