Theoretical studies for dynamical function of practical inerters

Abstract

This study aims to establish the fundamental theory of function of the practical inerters. Inerter is effective component for mechanical vibration system to control vibration frequency characteristics. Many studies related to inerter had been examined in the past. Although most of the previous studies are examined with ideal inerter which ignore mass and inertia of the devices themselve. We assume that the function of practical inerter can be regarded as the function of ideal inerter with two inertias connected to each terminal. We formulate four types of practical inerters: three types of torsional inerter constracted by planetary gear unit and one linear type inerter using rack and pinion gear mechanism. Re-arranging dynamic characteristics based on the assumption of the practical inerter function, it is confirmed that function of each practical inerter can be represented as the combination of two functions: one is ideal inerter function and the other is inertia-distribution function which is redistributed the inertia of the devices to each terminal. In addition, the inertia-distribution function could furthermore devide three subfunctions: first is inertia transfer, second is the directly connected inertia to the terminals, third is the indirectly connected inertia to the terminals. As the concluding remarks, fundamental theory of the practical inerter function is sucsessfully derived.

Keywords

• inerter
• theoretical formulation
• planetary gear
• rack and pinion
• torsional vibration system