摘要
多体系统动力学方程分为两类形式,即微分方程和微分-代数方程。这两类方程都是针对大位移系统,并且方程呈强非线性。为研究多体系统小位移或振动问题,从多体系统动力学方程出发,讨论微分-代数方程线性化计算机代数问题。利用完全笛卡尔坐标描述多刚体系统,建立多刚体系统动力学微分-代数方程。利用逐步线性化方法和计算机代数,分别对多体系统微分-代数方程的广义质量阵,约束方程和广义力阵在平衡位置附近进行Taylor展开。给出一种基于完全笛卡尔坐标的多体系统动力学微分-代数方程符号线性化方法。最后通过两个算例验证该方法的有效性。
The dynamics of a multi-body system can be described by using either a differential equation system or a differential/algebraic equation system, both being for the systems with large displacements and strong nonlinearity. To study vibration systems or the multi-body systems with small displacements efficiently, a computerized algebraic method for linearizing the equations of multi-body systems is discussed. Based on the fully Cartesian coordinates, a differential/algebraic equation system of multi-body system dynamics is obtained. A successive linearization technique together with a computerized algebraic method is used to simplify the model symbolically. Taylor series expansions of the generalized mass matrix, the constraint equations and the generalized force matrix of the equation system are obtained respectively in the neighboring regions of their equilibrium positions by using the symbolic linearization technique, so that the system can be dealt with in a simple and efficient way and some drawbacks of numerical perturbation methods are avoided. Two examples are given to show the effectiveness and correctness of the method.
出处
《工程力学》
EI
CSCD
北大核心
2004年第4期106-111,共6页
Engineering Mechanics
基金
国家自然科学基金资助项目(10272008)
北京市重点实验室开放课题资助项目
