基于Udwadia-Kalaba理论的隔振平台动力学研究

Dynamics Research of Isolation Platforms based on Udwadia-Kalaba Theory

针对微制造平台的隔振问题,基于Udwadia-Kalaba理论建立隔振平台的动力学模型,并研究其在人行激励下的动力学特性。针对固连结构和分散结构建立Udwadia-Kalaba动力学模型,通过MATLAB仿真分别得到固连结构和分散结构的各质点响应曲线。研究结果表明:基于Udwadia-Kalaba理论的动力学模型可以在不引入拉格朗日乘数的情况下求解;通过其固连结构与分散结构响应曲线的对比,可以得知其固连结构相对于分散结构模型更能达到明显的减振效果,而且该理论方法能较好地应用于微制造隔振平台振动问题求解。

Vibration isolation problem of the micro manufacturing platforms is studied.The dynamics models of the solid structure and the decentralized structure of the vibration isolation platform are established respectively based on Udwadia-Kalaba theory and their dynamic characteristics under pedestrian excitation are studied.The particle response curves of the two structures are obtained through MATLAB simulation.The result shows that the dynamic model based on the Udwadia-Kalaba theory can be solved without introducing Lagrange multipliers;the solid structure has more obvious damping effect than the decentralized structure.It is concluded that the proposed theoretical method can be effectively applied to the analysis of the dynamic problems of the micro manufacturing isolation platforms.