Critical damping design method of vibration isolation system with both fractional-order inerter and damper

Herein, the fractional derivative is firstly proposed to describe the constitutive relationship of a fluid inerter, and a dynamic model of a vibration isolation system (VIS) with both a fractional-order inerter and damper is established. The effects of the inerter parameters on the displacement transmissibility are analyzed; the results indicate that the fractional constitutive model can express the inertia and damping effects simultaneously, and the ratio between them can be changed by adjusting the derivative order. Furthermore, semi-analytical calculation methods of fractional critical damping, and optimal fractional critical damping and corresponding derivative order are proposed and verified through three examples.