多体系统动力学Riccati离散时间传递矩阵法

Riccati Discrete Time Transfer Matrix Method for Multibody System Dynamics

多体系统离散时间传递矩阵法是近年发展的多体系统动力学方法,因无须建立系统动力学方程、相关矩阵阶次低、计算速度快、建模程式化程度高等特点而倍受重视。为提高多体系统离散时间传递矩阵法的计算稳定性,本文将其与Riccati变换相结合,形成多体系统Riccati离散时间传递矩阵法,使空间传递两点边值问题化为初值问题、矩阵阶次降低。在Riccati变换时,选择了不同于振动力学Riccati传递矩阵法的合适中间变量,不扩大存储量的前提下进一步减小了计算时间。与多体系统离散时间传递矩阵法相比,提出的方法改善空间传递数值稳定性的同时不仅节省了计算时间,也提高了时间迭代计算稳定性。数值算例证明该方法对自由度十万的大系统有效、稳定性好,具有一定工程应用价值。

Discrete time transfer matrix method for multibody system dynamics （MS-DT-TMM）, a novel method for multibody dynamics simulation, has been developed in recent years. If using this method to simulate multibody dynamics, the global dynamical equations need not be developed, and such characteristics as lower order of global system matrix, fast computation speed, flexible modeling can also be obtained. To improve the numerical stability of MS-DT-TMM, in this investigation, MS- DT-TMM and Riccati transform are combined. Then a new method is formed, namely Riccati MS- DT-TMM. So boundary value problem of space transformation in MS-DT-TMM becomes the original value problem in Riccati MS-DT-TMM and the order of matrix can be reduced again. To shorten the computational time again, the intermediate variables of Riccati transfer matrix method used in vibration mechanics are improved without changing calculation precision and memory storage. Compared with MS-DT-TMM, if using the proposed method, the numerical stability not only in space field but also in time field can be improved and the CPU time can be economized synchronously. The numerical example of one hundred thousand degree of freedom system to validate the method has been given. It can show that the proposed method is a powerful tool for engineering application in multibody system dynamics field.