Analysis of Multiple Degrees of Freedom Vibration Isolation System Using the State Space Method

Abstract

This papers deals with fast solving method of natural frequency and vibration isolation coefficient of multiple degrees of freedom vibration isolation system. In the foundation of a mathematical model of vibration motion differential equation, a new state space method is derived and presented. Through transforming the vibration isolation differential equations into the state space equations, it is convenient to facilitate the solution of vibration isolation coefficient of vibration isolation system of multiple degrees of freedom with damping, by using the state space method and the MATLAB/Simulink module. Simulation results showed the result is consistent with the theory result. Simulation results also showed that with the help of damping, the maximal vibration isolation coefficient of x direction is lowered from 90 to 3.2 in the 5.31Hz, which eliminate the resonance phenomenon. In y and z direction, the maximal vibration isolation coefficient is also decreased from 78 to 2.4 and from 210 to 2.35. The state space method can find further applications on the selection of vibration isolation system and the evaluation of vibration isolation efficiency.