Study of dynamic breakdown of inerter and the improved design

Abstract

Inerter is a two-terminal dynamic element applied in vibration control systems. Based on the analogy between mechanical and electrical systems, an inerter corresponds to a capacitor. There is an electrical breakdown of a capacitor in electrical systems and there should also be a dynamic breakdown of an inerter in mechanical systems. This study focuses on the dynamic breakdown of an inerter. First, the definition and the expressive form of the dynamic breakdown of the inerter are introduced. The definition of the dynamic breakdown of an inerter in this study is that “the two terminals of the inerter come into contact”. When dynamic breakdown occurs, two terminals of the inerter impact on each other. To analyze the impact when the dynamic breakdown appears, a dynamic model is built. The expression of the impulse when the dynamic breakdown occurs is obtained, and an experimental system is established. Because of the experimental data collected by the force sensor, the impact force is far larger than the weight of the falling parts of the inerter. A design parameter for the inerter, the maximum allowable relative striking velocity, is proposed. Furthermore, the impact forces of the improved design, a new ball-screw inerter with mechanical diodes, are apparently reduced. The relationship between the impact force of the original inerter and the impact force of the improved design is also obtained and verified with experiments. It is concluded that there is a dynamic breakdown of the inerter and that the improved design of the inerter is effective to reduce the impact force when dynamic breakdown of the inerter occurs.