With the development of human history, technology is gradually developing breakthroughs. One of the most important periods that opened up the early beginnings of the modern era was the industrial revolution. During this time, the machinery industry has been formed, contributed an important role in supporting production activities. Machinery allows production of a variety of items. It is not only speed performance but also high efficiency beyond the human ability. In addition, machines perform better in long-term jobs and achieve higher consistency. The quality of work can be changed when human is influenced by emotional factors, health, etc. In addition, the machines help to carry out various dangerous tasks on behalf of humans. The machines are widely used in various fields such as: manufacturing, construction, agriculture, industry, mining, . Today, many machines are even designed to operate without controlling human. With the support of machines, the world becomes more modernizing and growing. Particularly in the context, the industrial revolution is developing on the world and affecting to the global economy. The research, manufacture and enhance longevity and ability to work of machinery that has contributed significantly to the industrial revolution. Shaft is one of the most important parts in machine. The Shaft is used to transmit torque and rotation from a part to another part of the machine through other machine parts assembly on the shaft such as the gear, belt, key, shaft couplings. The characteristic movement of shaft is rotary motion. During operation, the shaft is subjected to torque induced by the engine or system to the transmission shaft [21], [22], [25], [26], [28], [35]. In particular, the shafts and other components are generally made of elastic materials. So under the influence of torque, the axis will be subjected to twisting. This deformation is changed over time and repeated at each rotation cycle of the shaft that is called shaft oscillation. This oscillation is particularly harmful, undesirable. It is cause of fatigue damage and effects to the longevity and workability of the shaft and machine [21], [22], [25], [26], [ 28], [35]. Specifically, this deformation is cause of the vibration, machine noise, and fatigue damage of shaft. It effects not only to the shaft itself, but also damages other important machines mounted on the shaft. Thereby it induces damaging of the machine. The study to reduction of shaft vibration is an important and timely task [21], [22], [25], [26], [28], [35].