Active vibration suppression of a novel airfoil model with fractional order viscoelastic constitutive relationship. (13th October 2018) - Liu, Qi; Xu, Yong; Kurths, Jürgen
Abstract: This paper aims to investigate the active vibration suppression of a fractional two-degree-of-freedom viscoelastic airfoil (TDOFVA) model with a harmonic external force by means of the sliding mode control (SMC) scheme. The viscoelastic behavior is described as a fractional-order derivative, leading to a new fractional TDOFVA model. Subsequently, an averaging technique is extended to derive the amplitude-frequency relations, and its correctness is verified by Monte Carlo simulations. In addition, effects of the system parameters on the dynamics are explored. To achieve a vibration suppression, we convert the TDOFVA system into a series of fractional-order differential equations. Then, a SMC strategy is employed, in which a fractional-order integral sliding surface is presented and asymptotical stability analysis of the SMC is performed. Several numerical results are presented to illustrate the performances of the proposed SMC scheme, which indicate that the given SMC methodology is effective to realize a vibration suppression of the TDOFVA model. Highlights: A novel fractional viscoelastic airfoil model is proposed. Amplitude-frequency relations are obtained by an averaging technique. A jump phenomenon is observed and effects of system parameters are examined. Vibration suppression is achieved by a fractional-order sliding mode control.