考虑附加质量的旋转柔性梁动态可靠性分析

PDF(692 KB)

振动与冲击 ›› 2017, Vol. 36 ›› Issue (21) : 40-45.

论文

考虑附加质量的旋转柔性梁动态可靠性分析

靳红玲，王威，冯涛，郭成洋，陈军

作者信息 +

Dynamic Reliability Analysis of Rotating Flexible Beam With Tip Mass

JIN Hongling Wang Wei Feng Tao Guo Chengyang Chen Jun

Author information +

文章历史 +

摘要

在带有附加质量的旋转柔性梁系统动态可靠性分析中，为了提高其计算精度和计算效率，提出了一种基于单项式容积法(MCR, Monomial Cubature Rules)的随机响应面法(SRSM, Stochastic Response Surface Method)。该方法利用MCR的积分点作为样本点，并以此生成柔性梁系统动态响应的小样本对，基于这些样本对和SRSM回归理论，建立柔性梁系统动态响应可靠度隐式功能函数的代理模型，使用该代理模型对柔性梁系统进行动态响应可靠性分析。通过与传统的蒙特卡洛(MC, Monte Carlo)法和改进的概率配点法(ECM, Efficient Collocation Method)比较，表明了文中方法在柔性梁系统动态响应可靠性分析中的高效率和高精度。在取相同变异系数的条件下，柔性梁截面宽度参数的分散性对系统动态响应的可靠性影响较大。

Abstract

In order to improve computational accuracy and efficiency in dynamic reliability analysis of rotating flexible beam system with additional mass, a monomial cubature rules-based stochastic response surface method (MCR-SRSM) is proposed. A small set of sample pairs for flexible beam dynamic response are generated by taking the integral points of MCR as sample points. Based on these sample pairs and the regression theory of SRSM, the surrogate model of implicit feature function for systematic dynamic response reliability is established. The dynamic response reliability analysis of flexible beam system can be executed by the surrogate model. Simulation results show that the computational precision and efficiency of the proposed method are higher than those of known traditional Monte Carlo method and Efficient Collocation Method (ECM); under the same coefficients of variation, the dispersion of cross-sectional width parameter of the flexible beam has a significant effect on the dynamic response reliability.

Key words

flexible beam / tip mass / stochastic response surface method (SRSM) / Monomial Cubature Rules (MCR) / dynamic reliability

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用

靳红玲，王威，冯涛，郭成洋，陈军. 考虑附加质量的旋转柔性梁动态可靠性分析[J]. 振动与冲击, 2017, 36(21): 40-45

JIN Hongling Wang Wei Feng Tao Guo Chengyang Chen Jun. Dynamic Reliability Analysis of Rotating Flexible Beam With Tip Mass[J]. Journal of Vibration and Shock, 2017, 36(21): 40-45

参考文献

[1] 戎保, 芮筱亭, 王国平, 等. 多体系统动力学研究进展 [J]. 振动与冲击, 2011, 30(7): 178-187.
RONG Bao，RUI Xiao-ting，WANG Guo-ping，et al. Developments of studies on multibody system dynamics [J]. Journal of Vibration and Shock, 2011, 30(7): 178-187.
[2] 杜超凡, 章定国, 洪嘉振, 等. 径向基点插值法在旋转柔性梁动力学中的应用 [J]. 力学学报, 2015, 47(2): 279-288.
DU Chao-fan, ZHANG Ding-guo, HONG Jia-zhen, et al. A meshfree method based on radial point interpolation method for the dynamic analysis of rotating flexible beams[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2): 279-288.
[3] 王建明, 刘又午, 洪嘉振. 大范围刚体运动对柔性梁模态形函数的影响分析 [J]. 中国机械工程, 2000, 11(6): 640-643.
WANG Jian-ming, LIU You-wu, HONG Jia-zhen. Analysis on the mode shapes of flexible beams affected by large overall motion [J]. China Mechanical Engineering, 2000, 11(6): 640-643.
[4] 杨绿峰, 杨显峰, 余波, 等. 基于逐步回归分析的随机响应面法 [J]. 计算力学学报, 2013, 30(1): 88-93.
YANG Lu-feng, YANG Xian-feng, YU Bo, et al. Improved stochastic response surface method based on stepwise regression analysis[J]. Chinese Journal of Computational Mechanics, 2013, 30(1): 88-93.
[5] Ji Y. Fuzzy Reliability Analysis of Nonlinear Structural System Based on Stochastic Response Surface Method [J]. Advanced Materials Research, 2014, 912-914: 1268-1271.
[6] Zhao Q H, Chen X K, Ma Z D, et al. Reliability-Based Topology Optimization Using Stochastic Response Surface Method with Sparse Grid Design [J]. Mathematical Problems in Engineering, 2015, 2015: 1-13.
[7] 赵宽, 陈建军, 曹鸿钧, 等. 随机参数双连杆柔性机械臂的可靠性分析 [J]. 工程力学, 2015, 32(2): 214-220.
ZHAO Kuan, CHEN Jian-jun, CAO Hong-jun, et al. Reliability analysis on two-link flexible robot manipulator with random parameters [J]. Engineering Mechanics, 2015, 32(2): 214-220.
[8] Kim N H, Kim Y J. Safety envelope for load tolerance and its application to fatigue reliability design [J]. Journal of Mechanical Design, 2006, 128(4): 919-927.
[9] Tatang M A, Pan W, Prinn R G, et al. An efficient method for parametric uncertainty analysis of numerical geophysical models [J]. Journal of Geophysical Research Atmospheres, 1997, 102(18): 21925-21932.
[10] Isukapalli S S, Roy A, Georgopoulos P G. Efficient sensitivity/uncertainty analysis using the combined stochastic response surface method and automated differentiation: application to environmental and biological systems [J]. Risk Analysis, 2000, 20(5): 591-602.
[11] 胡冉, 李典庆, 周创兵, 等. 基于随机响应面法的结构可靠度分析[J]. 工程力学, 2010, 27(9): 192-200.
HU Ran, LI Dian-qing, ZHOU Chuang-bing, et al. Structural reliability analysis using stochastic response surface method [J]. Engineering Mechanics, 2010, 27(9): 192-200.
[12] Li D Q, Chen Y F, Lu W B, et al. Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables [J]. Computers & Geotechnics, 2011, 38(1): 58-68.
[13] 蒋水华, 李典庆, 周创兵. 随机响应面法最优概率配点数目分析 [J]. 计算力学学报, 2012, 29(3): 345-351.
JIANG Shui-hua, LI Dian-qing, ZHOU Chuang-bing. Optimal probabilistic collocation points for stochastic response surface method [J]. Chinese Journal of Computational Mechanics, 2012, 29(3): 345-351.
[14] Stroud A H. Approximate calculation of multiple integrals [M]. N J: Prentice-Hall, Englewood Cliffs, 1971．
[15] 韦东来, 崔振山, 陈军. 混沌多项式新求解及其在板料成形性容差预测中的应用 [J]. 机械工程学报, 2009, 45(8): 261-265.
WEI Dong-lai, CUI Zhen-shan, CHEN Jun. New solution for polynomial chaos expansion and application in tolerance prediction for stamping process[J]. Jounal of Mechanical Engineering, 2009, 45(8): 261-265.
[16] Wei D, Cui Z, Chen J. Robust optimization based on a polynomial expansion of chaos constructed with integration point rules [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2009, 223(5): 1263-1272.
[17] 靳红玲, 陈建军, 赵宽, 等. 空间柔性梁的随机动力学分析 [J]. 西安电子科技大学学报, 2015, 42(4): 47-52.
JIN Hong-ling, CHEN Jian-jun, ZHAO Kuan et al. Stochastic dynamic analysis of spatial flexible beam [J]. Journal of Xidian University, 2015, 42(4): 47-52
[18] 韦东来. 汽车覆盖件成形工艺的稳健优化与容差分析 [D]. 上海: 上海交通大学, 2009.
[19] 靳红玲, 陈建军, 郭康权. 考虑附加质量的旋转柔性梁的随机动力学分析 [J]. 振动工程学报, 2015, 28(6): 960-965.
JIN Hong-ling, CHEN Jian-jun, GUO Kang-quan. Stochastic dynamic analysis of spatial flexible beam with tip mass [J]. Journal of Vibration Engineering, 2015, 28(6): 960-965.