随机空间柔性多体系统动力学分析
郭祥, 靳艳飞, 田强
摘要：轻质，高精度的柔性多体系统被广泛应用于实际工程领域中。由于实际设计公差,制造误差及环境温度等多种不确定因素的存在，使得柔性多体系统的结构参数(物理参数和几何参数)表现出随机性。具有随机结构参数的动力学模型能够客观地反映出真实系统的动力学行为，且结构参数的不确定性对空间柔性多体系统动力学响应的影响是不容忽视的。针对具有多个随机参数的空间柔性多体系统，提出了一种基于广义alpha算法的非侵入式随机柔性多体系统动力学计算方法。采用绝对节点坐标公式(absolute node coordinate formulation, ANCF)来描述柔性体，推导建立多体系统动力学模型。利用混沌多项式展开(polynomial chaos expansion, PCE)法构建系统随机动力学方程的代理模型，然后将随机响应面法(stochastic response surface method， SRSM)嵌入广义-alpha方法中，分别采用改进抽样的回归方法 (regression method of improved sampling， RMIS)和单项求容积法则(Monte Carlo simulation， MCR)来确定样本点。将数值计算结果与蒙特卡洛模拟(Monte Carlo simulation， MCS)结果进行对比，验证了所提算法的有效性。在相同的定积分精度的条件下，根据单项求容积法则确定的样本点的计算结果稳定性更强，且其计算效率更高。
关键词：
Xiang Guo, Yanfei Jin, Qiang Tian
Abstract: Flexible multibody systems with light weight and high precision are widely used in practical engineering. The structural parameters of the flexible multibody system show randomness due to the existence of many uncertain factors such as actual design tolerance, manufacturing error and environmental temperature. The dynamic model with random structural parameters can objectively reflect the dynamic behavior of the real system, and the influence of the uncertainty of structural parameters on the dynamic response of the spatial flexible multibody system cannot be ignored. A non-intrusive calculation method is proposed based on the generalized-alpha algorithm to study the dynamic response of stochastic spatial flexible multibody system with multiple random parameters. The absolute node coordinate formulation ANCF is used to describe the flexible body, and the dynamic model of multibody system is established. The polynomial chaos expansion PCE method is used to construct the surrogate model of the stochastic dynamics equation of the system. Then, the stochastic response surface method SRSM is embedded into the generalized-alpha method. The regression method of improved sampling RMIS and the monomial cubature rules MCR are used to determine the sample points respectively. The numerical results are compared with those of Monte Carlo simulation MCS, and the validity of the proposed algorithm is verified. Under the condition of the same definite integral precision, the calculation results of sample points determined by the monomial cubature rules are more stable and the calculation efficiency is higher.
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原文链接：https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-52-6-1730.shtml
