Analysis of the characteristics of variable-order fractional viscoelastic oscillator under impact loading

As a critical bridge connecting material properties and dynamic behaviors of system, the viscoelastic oscillator is important in engineering practice. By embedding the variable-order fractional (VOF) constitutive model into viscoelastic oscillator, a variable-order fractional viscoelastic oscillator (VOFVO) dynamic model under impact loading is established. The methods of Laplace transform method, hybrid of block-pulse function and Taylor polynomial are used to solve the system responses of VOFVO dynamic model in time and frequency domains. The Split Hopkinson Pressure Bar (SHPB) impact experiment is conduced. Through a comparative analysis with the Constant fractional-order Kelvin-Voigt (CFKV) model and the Zhu-Wang-Tang nonlinear thermo-viscoelastic constitutive (ZWT) model, the accuracy of the VOF model is validated. The results show that the VOFVO in the high elastic stage Ⅱ has the best damping characteristics with the smallest vibration amplitude, the shortest vibration period, and the fastest vibration attenuation. In the frequency domain, the resonance peaks of VOFVO responses in the three stages appear near a frequency ratio of one. The natural frequency $w_n$, damping ratio $\xi$ and geometric factor $\kappa$ are negatively correlated with the VOFVO responses. The first amplitude decreases from 0.017 to 0.0005 as the system parameters increased. Compared to the damping ratio $\xi$, the natural frequency $w_n$ has a more significant impact on the system responses. The geometric factor $\kappa$ needs to be determined by comprehensively considering the smaller vibration amplitudes and rational structural configuration.