中文摘要：

研究了含随机参数空间柔性梁进行大范围运动的动力响应问题。基于虚功原理建立了随机参数空间柔性梁的动力学模型，利用单项式容积法的积分点作为混沌多项式的配点，通过可变秩法和回归法求解混沌多项式系数，进而得到柔性梁变形位移动力响应的数字特征。以物理参数和几何参数具有随机性的自旋空间柔性梁为例，获得其动力响应统计意义下的解，通过与 Monte Carlo 法和高效回归法模拟结果比较，验证了文中方法的正确性和有效性。计算结果表明，随机参数的分散性对柔性梁的动力响应的影响不可忽视，利用含随机参数的动力学模型能客观地反映出空间柔性梁的动力学行为。

英文摘要：

The uncertainty dynamic response of a spatial flexible beam with large overall motion is investigated . The stochastic differential equations of a three‐dimensional beam with large overall motion are derived by using the virtual work principle . The polynomial chaos method and monomial cubature rules are applied to derive a set of completely implicit differential equations . Then the polynomial coefficients are obtained by the variable order method and regression method so as to find the numerical characteristics of the response . As an illustrating example , dynamic modeling of a spatial flexible beam by considering the probabilistic of geometric and physical parameters is presented . The accuracy and efficiency of the method are verified by comparing the results with those given by the Monte Carlo simulation method . The results show that the probabilistic parameters have a significant effect on the dynamic response of the flexible beam and that the dynamic modeling with probabilistic parameters can objectively reflect the dynamic behavior of the objective systems .