One-degree-of-freedom Distributed-order Vibration and Resonance

Abstract

The response of a one-degree-of-freedom distributed-order vibration system to a harmonic driving was considered. For the steady case, the lower limit of integration in the definition of fractional derivatives was taken as negative infinity. The response amplitude, phase difference between driving and response, and the effects of distributed-order derivative on damping and resonance were investigated in detail. The results display that the parameter in distributed-order derivative can effectively characterize the viscoelasticity.