Dynamic performance of an inerter vibration isolator under base excitation considering friction

The inerter is a vibration control element related to the acceleration between its two ends, which can increase inertia through a speed-increasing mechanism. Applying the inerter to a vibration isolator can enhance its low-frequency vibration isolation performance. Frictional force always exists in the high-speed mechanism of the inerter. Even if it is not large, its influence on the dynamic performance of the low-speed end cannot be ignored. This study analyzes the force of a ball-screw inerter using the kinetic energy theorem. The inerter force is then expanded into the first-order Taylor approximation, from which the inerter coefficient and apparent friction coefficient are determined. Based on the approximate formula of the inerter force, the nonlinear dynamic model and its corresponding dynamic equation for the inerter vibration isolator under base excitation are established. The nonlinear dynamic equation is then solved by averaging method, and the approximate analytical solutions for the relative displacement, absolute displacement, and displacement transmissibility are obtained. The analysis results show that a larger apparent friction coefficient reduces the resonance peaks of the displacement transmissibility and relative displacement amplitude, but it slightly increases the initial vibration isolation frequency, as well as the resonance and valley frequencies of the displacement transmissibility and relative displacement. Increasing the inerter-mass ratio can reduce the resonance frequency and initial vibration isolation frequency, thereby broadening the vibration isolation frequency domain. When friction is considered, increasing the inerter-mass ratio can suppress the resonance peaks of the displacement transmissibility and relative displacement.