Application of the fractional oscillator model to describe damped vibrations

Abstract

We consider a model of damped vibrations based on fractional differentiation. The model given is completelyconsistent with the classical model of vibration with viscous damping. We find the relation between the order of fractionaldifferentiation in the equation of motion and Q-factor of an oscillator. The proposed approach seems more appropriatefor the physical nature of the described system. The experiment with a vibrating piezoelectric plate, performed as partof the study, showed good agreement with the model and confirmed that the fractional oscillator model can be used todescribe strongly damped vibrations.