The mathematical principles of vibration reductor

Abstract

In engineering and technology, it is often demanded that self-oscillation be eliminated so that the equipment or machinery may not be damaged. In this paper, a mathematical model for reducing vibration is given by the following equations:

$$\ddot x_1 + \varphi \left( {\dot x_1 } \right) + k_1 \left( {x_1 - x_2 } \right) = 0,{\text{ }}\ddot x_2 + c\dot x_1 + k_2 \left( {x_2 - x_1 } \right) = 0$$

We have discussed how to choose suitable parameters c₁, k₁, k₂ of equations(*), so as to make the zero solution to be of global stability. Several theorems on the global stability of the zero solution of equations(*) are also given.