Response of fractional Maxwell viscoelastic oscillator subjected to impact load

摘要

The prediction for the impact behavior of viscoelastic oscillator (VEO) has a great significance. The fractional Maxwell viscoelastic oscillator (FMVEO) model under impact load is derived by integrating the fractional Maxwell constitutive model into the system vibration equation and further involving the geometric factors of the isolators. The numerical algorithm based on Chebyshev operational matrix is derived. The Split Hopkinson Pressure Bar (SHPB) experiment is conducted to validate the proposed model. The results indicate that FMVEO can fully describe impact properties of the viscoelastic oscillator. The fractional orders alpha and beta are critical to the elasticity-viscosity component of FMVEO and the first amplitude of the impact response, respectively. The response of FMVEO displays an under-damped state for alpha <= 0.5 and over-damped state for alpha > 0.5. FMVEO degenerates into a pure-elastic system for alpha = 0 and evolves into a pure-viscous system for alpha = 1. In frequency domain, there are resonant peaks for the amplitude-frequency response for alpha <= 0.5, while no pronounced peaks exist for alpha > 0.5. The fractional order beta displays a positive correlation with the first amplitude and a weakly negative correlation with the damping. The geometric factor kappa should be taken into full consideration in two ways, the relatively small amplitude and the limited installation space, which shows the significant effect of the geometric element on the system response.