含随机参数的空间柔性梁动力学模型

Uncertainty dynamic modeling of spatial flexible beam with probabilistic parameters

研究含随机参数空间柔性梁作大范围运动的动力响应问题。基于虚功原理建立随机参数空间柔性梁动力学模型,利用多项式混沌结合高效回归法将其转化为完全隐式纯微分方程,通过可变秩法获得响应函数展开多项式系数,进而获得柔性梁变形响应量数字特征。以物理、几何参数具有随机性自旋空间柔性梁为例,获得动力响应统计意义下的解,通过与Monte Carlo法结果比较,验证该方法的正确性及有效性。计算结果表明,利用随机参数的动力学模型能客观反映空间自旋柔性梁动力学行为;部分随机参数的分散性对柔性体动力响应影响不可忽视。

The uncertain dynamic response of a spatial flexible beam with large overall motion was investigated. The stochastic differential equation of a three-dimensional beam with large overall motion was derived using the virtual work principle.The polynomial chaos method combined with a regression-based collocation method was applied to derive a set of completely implicit differential equations.The resulted system of deterministic equations was then solved using the variable rank method to obtain the numerical characteristics of the response.For illustration,the dynamic modeling of a spatial spinning beam with probabilistic geometric and physical parameters was considered.The accuracy and efficiency of the method were verified by comparing the results with those given by the Monte Carlo simulation method.The results indicate that probabilistic parameters affect the dynamic response of the flexible body.It is expected that the dynamic modeling with probabilistic parameters can objectively reflect the actual dynamic behavior of elastic systems.