Vibration Control Using Vibration Energy Transmissibility of Two-Degree-of-Freedom System

This study focuses on the energy transmissibility, which is called coupling loss factor (CLF) in Statistical Energy Analysis (SEA) framework, for two degree of freedom vibration system. The aim of this study is to obtain a new interpretation of the energy transfer viewpoint of the phenomena represented by the two-degree-of-freedom vibration system and to utilize it for vibration control and structural design. In this paper, the energy transfer characteristics of one-degree-of-freedom and two-degree-of-freedom vibration systems are explicitly derived from the equations of motion under broadband excitation through the energy (power) equilibrium and the frequency average concept. And then it is shown that the derived energy transmissibility can be described by a mathematical equation and is a single value. The transmissibility is determined by three parameters, which are the properties concerning each two uncoupled one degree of freedom vibration system, the uncoupled natural angular frequencies, the damping and the coupling properties. Then the energy transmissibility can be easily used for understanding phenomena described by the two degree of freedom systems and for control and design them. Furthermore, as an example of vibration control based on the energy transmissibility, the reduction of engine shake in automobiles is presented, and its effectiveness is compared and discussed with the results in the reference.