Impact response analysis of vibration system with inerter

Abstract

This research investigates using an inerter system to control the impact-induced vibration response of a single degree of freedom(SDOF) and two degrees of freedom(TDOF) vibration system. An analytic model of the SDOF system with an inerter is first derived, and simulation is performed to compare the inerter performance in suppressing the maximum acceleration response under shock load. Next, a more complex TDOF vibration model with an inerter is derived, and the effectiveness of the inerter in reducing the large acceleration amplitude is evaluated. The energy analysis is conducted to investigate the energy transfer mechanism during impact. The simulation study shows that one can significantly decrease the maximum acceleration response with an appropriate selection of the inerter parameters. For the SDOF vibration system with an inerter, response reduction is greatly influenced by the system’s natural frequency. In the TDOF vibration system, the maximum acceleration response attenuation is caused by two factors. For a large inerter radius, the acceleration response reduction is mainly influenced by energy transfer between unsprung and inerter mass. However, for a big inerter mass, attenuation of the acceleration response is caused by decreasing the system’s natural frequency. It is observed from the simulation that the maximum acceleration response can be reduced up to 35% by adjusting the inerter radius of gyration. Furthermore, the optimum condition for reducing the acceleration response occurs when the inerter mass is half the unsprung mass ( m i = 0.5 m u). An experimental study is conducted to validate the simulation results.