Abstract：Aiming at linear structures under combined action of static-Gaussian random loads, probabilistic distribution of structure’s Von Mises stress process was examined.Then the central Chi-squared distribution was used to approximately study Von Mises stress calculation under a certain cumulative probability level of 99.73%.Further, a strength evaluation method was proposed under static-random vibration combined condition.Based on a numerical example, the simulation results and calculation efficiency using the proposed method were compared with those using Monte Carlo method.The results showed that the proposed method has higher accuracy and calculation efficiency.Finally, two commonly used engineering approximation methods were examined to mathematically prove engineering approximation methods being always conservative, and provide a theoretical basis for existing methods.
郝雨，冯加权,胡杰. 静力-随机振动复合工况下Von Mises应力的概率分布及强度评估[J]. 振动与冲击, 2020, 39(5): 188-193.
HAO Yu, FENG Jiaquan, HU Jie. Probabilistic distribution of Von Mises stress and strength evaluation of structures under static-random vibration combined condition. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(5): 188-193.
[1] Tibbits P A. Percentiles of von Mises Stress from Combined Random Vibration and Static Loading by Approximate Noncentral Chi Square Distribution[J]. Journal of Vibration and Acoustics, 2012, 134(4): 795-803.
[2] Rajmeny P K, Singh U K, Sinha B K P. Predicting rock failure around boreholes and drives adjacent to stopes in Indian mines in high stress regions[J]. Int. J. Rock Mech. Min. Sci. 2002,39(2): 151–164.
[3] 吴建国，李海波，张琪等. 综合离心环境试验技术研究进展[J]. 强度与环境，2014,41(1): 1-9.
Wu Jianguo, Li Haibo, Zhang Qi, et al. Advances in synthesis centrifugal environment test[J]. Structure & Environment Engineering, 2014,41(1):1-9.
[4] Segalman D J, Fulcher C W G, Reese G M, et al. Efficient method for calculating RMS von M ises stress in a random vibration environment[C]. Proceedings of the International Modal Analysis Conference, Bethel, USA, 1998.1: 117-123.
[5] Quaranta G, Mantegazza P. Randomly excited structures reliability by means of the von Mises stress response[C]. XVI Congresso Nazionale AIDAA, Palermo Italy, 2001.
[6] Fuente E. Von Mises stresses in random vibration of linear structures[J]. Computers and Structures, 2009(87): 1253-1262.
[7] 金奕山，李琳. 随机振动载荷作用下结构Von Mises应力过程的研究[J]. 应用力学学报, 2004,21(3): 13-16.
Jin Yishan, Li Lin. Probability density function of von Mises stress for structures undergoing random excitations[J]. Chinese Journal of Applied Mechanics, 2004,21(3): 13-16.
[8] Fackler W. Equivalence techniques for vibration testing[R]. 1972: SVM-9.
[9] Luhrs H. Random vibration effects on piece part applications[C]. Proceedings of the Institute of Environmental Sciences, Los Angeles CA, 1982.
[10] Pearson E S. Note on an approximation to the distribution of non-central χ2[J]. Biometrika, 1959, 46:364.
[11] Kotz S, Johnson N L, Boyd D W. Series representations of distributions of quadratic forms in normal variables ii. Non-central case[J]. The Annals of Mathematical Statistics, 1967(38): 838-848.
[12] Liu H, Tang Y Q, Zhang H H. A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables [J]. Computational Statistics and Data Analysis, 2009(53): 853-856.
[13] Imhof J P. Computing the distribution of quadratic forms in normal variables[J]. Biometrica, 1961(48): 419-426.
[14] Solomon H, Stephens M A. Distribution of a sum of weighted chi-square variables[J]. Journal of American Statistical Association, 1977(72): 881-885.
[15] MATLAB Statistic Toolbox Users’ Guide[M]. Mathworks Inc., 2009.
[16] 郝雨，冯加权，胡杰. 一种近似的随机振动强度校核方法[C]. 中国核学会核工程力学分会学术年会，成都，2018.
Hao Yu, Feng Jiaquan, Hu Jie. An approximate method for strength checking under random vibration[C]. Annual of China Nuclear Society-Nuclear Engineering Mechanics, Chengdu, 2018.
