Critical damping characteristics of a SDOF system with fractional derivative of a wide range of order

Abstract

In this study, vibration characteristics of a single-degree-of-freedom linear oscillator with the fractional order derivative are examined in terms of the critical damping over a wide range of the order of the fractional derivative by using numerical analysis. Two types of the definitions of the critical damping used in the previous studies are considered. It is shown that (i) the critical viscoelastic damping ratio changes according to the order of the fractional derivative and its minimum value for both types of the critical damping is less than 1; (ii) no critical viscoelastic damping ratio is observed in a certain range of the order; (iii) the difference in the existence of the critical damping between the oscillators with the derivative of order 1/3 and 2/3 is caused by the change of the behavior of a component of the response corresponding to one of the roots of the characteristic polynomial for the oscillator. Finally, the impulse response characteristics are classified into three classes depending on the order of the fractional derivative and viscoelastic damping ratio of the oscillator.

Keywords

• fractional damping
• impulse response
• critical damping
• numerical analysis
• indicial polynomial