Vibration Analysis of Inverted Rubber Pendulum and Application to the Dynamic Absorber.

Abstract

It is important to reduce vibration for resonant vibration phenomena of vibration systems such as some structure, building, and machine equipment. This paper presents detailed analysis of the inverted rubber pendulum for a simple vibration reduction method. The advantage of the passive damping device using the inverted rubber pendulum is that 1. The structure is very simple, 2. The system constitution is low-cost, and 3. The damping performance can be estimated by vibration analysis of the equivalent model. Then it is possible to present basic data as a design creterion for system construction. The inverted rubber pendulum consists of a mass and a rubber element with visco-elasticity. A modulus of longitudinal elasticity of the rubber element is assumed to be rubber with complex modulus of longitudinal elasticity E*=ER(1+jε). Applying the equivalent model of complex modulus of longitudinal elasticity, vibration characteristics of the damped free vibration and forced vibration of the inverted rubber pendulum are made clear, and the natural angular frequency of one is derived qualitatively by this theoretical computation. And this theoretical technique can be applied to the dynamic absorber. By this theory, it is possible to obtain optimum tuning condition and optimum loss factor using the fixed point theory.