Structural dynamics modeling and analysis based on Lagrange equations of energy principle

Abstract

In order to analyze the structural dynamics and realize dynamically optimum design, it is necessary to establish dynamic analytic model that can be simulated the structure. Based on Lagrange equations and energy principle, a method of establishing the dynamic model of structure considering joint dynamic characteristics is presented and analyzed. The motion coordinates of each component are selected according to the structure characteristics and the vibration displacement for each component in exciting test, and the equivalent dynamic parameters of each joint are calculated according to the way and condition of the joint by applying the general joint surface dynamic data. The Lagrange equations for mechanical structure are derived and described, and the dynamics equations of structure are obtained. As a practical example, a vertical milling machine is modeled and analyzed. The machine is represented by a dynamic model with 19 degrees of freedom, the dynamic performance computations, harmonic response and modal analysis are completed and the results agree with that of exciting test. The dynamic model can well simulate the actual structure dynamic characteristics, and the method is effective and applicable to engineering.