基于概率密度演化的铅芯橡胶支座水平等效刚度不确定性
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摘要
铅芯橡胶支座水平等效刚度是影响水平隔震效果的主要指标,其材料特性及尺寸参数等在制作过程中存在变异性,因而引起支座水平等效刚度的不确定性。本文考虑铅芯橡胶支座四个尺寸参数和四个材性参数的变异性,引入变异系数,基于概率密度演化方法得到支座水平等效刚度的概率密度曲线(PDF),引入保证率,分析参数变异对支座水平等效刚度不确定性的影响。结果表明:尺寸参数中的单层橡胶厚、支座直径、铅芯直径,材性参数中的橡胶剪切模量、铅芯屈服强度,对PDF曲线离散性影响较大,相应的刚度结果保证率较小,不确定性较大。除钢板层厚度外,尺寸参数变异时PDF曲线的离散性均大于材性参数变异时情况,其引起的水平等效刚度不确定性普遍较大。本文研究单参数独立变异对水平等效刚度不确定性的影响,为后续多参数综合变异时的相关研究进行前期探索。
The equivalent horizontal stiffness is one of the main factors which influence the isolation performance of lead rubber bearings. Uncertainty of the equivalent horizontal stiffness usually exists due to the uncertainty of the material properties and geometry parameters during manufacture. Variation of four geometry parameters and four material property parameters are focused on in this research, and variation coefficient is introduced to consider their variability. Probability density function(PDF) of the equivalent horizontal stiffness is obtained with the probability density evolution method. Assurance rate is introduced to study the influence of the parameters variability on the uncertainty of the equivalent horizontal stiffness. Analysis results show that PDF discreteness of the thickness of single rubber layer, bearing diameter and lead core diameter in geometry parameters, the shear modulus of the rubber and the yield strength of the lead core in material property parameters is relatively larger. Assurance rate of stiffness is smaller. The uncertainty level of stiffness is higher. Except the steel plate thickness, PDF discreteness and uncertainty level of geometry parameters is larger than that of the material property parameters. In this paper, the influence of single parameter variation on the uncertainty of horizontal equivalent stiffness is studied. It is a preliminary study for the subsequent research work on the comprehensive variation of multiple parameters.
The equivalent horizontal stiffness is one of the main factors which influence the isolation performance of lead rubber bearings. Uncertainty of the equivalent horizontal stiffness usually exists due to the uncertainty of the material properties and geometry parameters during manufacture. Variation of four geometry parameters and four material property parameters are focused on in this research, and variation coefficient is introduced to consider their variability. Probability density function(PDF) of the equivalent horizontal stiffness is obtained with the probability density evolution method. Assurance rate is introduced to study the influence of the parameters variability on the uncertainty of the equivalent horizontal stiffness. Analysis results show that PDF discreteness of the thickness of single rubber layer, bearing diameter and lead core diameter in geometry parameters, the shear modulus of the rubber and the yield strength of the lead core in material property parameters is relatively larger. Assurance rate of stiffness is smaller. The uncertainty level of stiffness is higher. Except the steel plate thickness, PDF discreteness and uncertainty level of geometry parameters is larger than that of the material property parameters. In this paper, the influence of single parameter variation on the uncertainty of horizontal equivalent stiffness is studied. It is a preliminary study for the subsequent research work on the comprehensive variation of multiple parameters.
引文
[1] 王光远. 论不确定性结构力学的发展[J]. 力学进展, 2002, 32(2):205-211.WANG Guangyuan. On the development of uncertain structural mechanics [J]. Advances in Mechanics, 2002,32(2): 205-211.(in Chinese)
[2] 李杰, 陈建兵. 随机振动理论与应用新进展[M]. 上海: 同济大学出版社, 2009: 60-94.LI Jie, CHEN Jianbing. Advances in theory and applications of random vibration [M]. Shanghai: Tongji University Press, 2009: 60-94. (in Chinese)
[3] 李杰, 陈建兵. 随机动力系统中的概率密度演化方程及其研究进展[J]. 力学进展, 2010,40(2): 170-188.LI Jie, CHEN Jianbing. Probability density evolution equation of stochastic dynamical system and research advances [J]. Advances in Mechanics, 2010, 40(2): 171-188. (in Chinese)
[4] 李杰, 陈建兵. 概率密度演化理论的若干研究进展[J]. 应用数学和力学, 2017, 38(1): 32-43.LI Jie,CHEN Jianbing. Some new advances in the probability density evolution method[J]. Applied Mathematics and Mechanics, 2017, 38(1): 32-43.(in Chinese)
[5] 王曙光, 施凯琳, 杜东升, 等. 基于概率密度演化的隔震结构随机地震响应[J]. 地震工程与工程振动, 2013, 33(2): 168-175.WANG Shuguang, SHI Kailin, DU Dongsheng, etc. Stochastic seismic responses of isolated structure based on probability density evolution method [J]. Earthquake Engineering and Engineering Dynamics, 2013, 33(2):168-175.(in Chinese)
[6] 刘令波. 基于概率密度演化的非线性随机结构可靠度分析[D]. 大连:大连理工大学, 2013.LIU lingbo. Reliability Analysis of Nonlinear Stochastic Structures Based on Probability Density Evolution[D]. Dalian: Dalian University of Technology, 2013. (in Chinese)
[7] 梅真, 郭子雄, 高毅超. 基于模型结构振动台试验的概率密度演化方法验证[J]. 工程力学, 2017, 34(3): 54-61.MEI Zhen, GUO Zixiong, GAO Yichao. Validation of the probability density evolution method based on shaking table tests of a model structure [J]. Engineering Mechanics, 2017, 34(3): 54-61. (in Chinese)
[8] 李杰. 随机结构系统-分析与建模[M]. 北京: 科学出版社, 1996.LI Jie. Stochastic structure system-analysis and modeling[M]. Beijing: Science Press, 1996. (in Chinese)
[9] 朱玉华, 庄文娟, 黄海荣. 铅芯橡胶隔震支座水平刚度影响因素数值分析[J]. 结构工程师, 2009, 25(6): 66-71.ZHU Yuhua, ZHUANG Wenjuan, HUANG Hairong. Simulation analysis on effects of horizontal stiffness in lead-rubber bearings [J]. Structural Engineers, 2009, 25(6):66-71. (in Chinese)
[10] 艾方亮, 朱玉华, 任祥香. 不同尺寸铅芯橡胶隔震支座力学性能的有限元分析[J]. 结构工程师, 2016, 32(6): 74-79.AI Fangliang, ZHU Yuhua, REN Xiangxiang. FEA study on mechanical properties of lead-rubber bearings with different diameters [J]. Structural Engineers, 2016, 32(6):74-79.(in Chinese)
[11] 王建强, 辛伟, 李政, 等. 铅芯橡胶支座剪切性能影响因素分析[J]. 世界地震工程, 2014(3): 77-81.WANG Jianqiang, XIN Wei, LI Zheng, et al. Influence factor on shear properties of lead-rubber bearings [J]. World Earthquake Engineering, 2014(3):77-81.(in Chinese)
[12] 董玉勇, 陆飞, 张富有. 天然叠层橡胶支座水平刚度的概率统计分析[J]. 科学技术与工程, 2013, 13(11): 3158-3161.DONG Yuyong, LU Fei, ZHANG Fuyou. Study on characteristics of probability and statistics of rubber isolation bearing’s horizontal stiffness[J]. Science Technology and Engineering, 2013, 13(11):3158-3161.(in Chinese)
[13] Ahmadipour M, Alam M S. Sensitivity analysis on mechanical characteristics of lead-core steel-reinforced elastomeric bearings under cyclic loading[J]. Engineering Structures, 2017, 140: 39-50.
[14] 薛彦涛, 常兆中, 高杰. 隔震建筑设计指南[M]. 北京: 中国建筑工业出版社, 2016.XUE Yantao, CHANG Zhaozhong, GAO Jie. Designin guide for isolated buildings. Beijing: China Building Industry Press, 2016. (in Chinese)
[15] Chen J, Yang J, Li J. A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters[J]. Structural Safety, 2016, 59: 20-31.
[16] 陈建兵, 李杰. 随机结构动力可靠度分析的极值概率密度方法[J]. 地震工程与工程振动, 2004, 24(6): 39-44.CHEN Jianbing, LI Jie. The extreme value probability density function based method for dynamic reliability assessment of stochastic structures[J]. Earthquake Engineering and Engineering Dynamics, 2004, 24(6):39-44. (in Chinese)Uncertainty of equivalent horizontal stiffness of lead-rubber bearings based on probability density evolution method XUE Bin, ZHU Yuhua, HE Yi, et al.(145)Study on residual column drift rate collapse criteria of continuous girder bridge based on IDA CAI Xiaoyu, TIAN Shizhu(153)
[2] 李杰, 陈建兵. 随机振动理论与应用新进展[M]. 上海: 同济大学出版社, 2009: 60-94.LI Jie, CHEN Jianbing. Advances in theory and applications of random vibration [M]. Shanghai: Tongji University Press, 2009: 60-94. (in Chinese)
[3] 李杰, 陈建兵. 随机动力系统中的概率密度演化方程及其研究进展[J]. 力学进展, 2010,40(2): 170-188.LI Jie, CHEN Jianbing. Probability density evolution equation of stochastic dynamical system and research advances [J]. Advances in Mechanics, 2010, 40(2): 171-188. (in Chinese)
[4] 李杰, 陈建兵. 概率密度演化理论的若干研究进展[J]. 应用数学和力学, 2017, 38(1): 32-43.LI Jie,CHEN Jianbing. Some new advances in the probability density evolution method[J]. Applied Mathematics and Mechanics, 2017, 38(1): 32-43.(in Chinese)
[5] 王曙光, 施凯琳, 杜东升, 等. 基于概率密度演化的隔震结构随机地震响应[J]. 地震工程与工程振动, 2013, 33(2): 168-175.WANG Shuguang, SHI Kailin, DU Dongsheng, etc. Stochastic seismic responses of isolated structure based on probability density evolution method [J]. Earthquake Engineering and Engineering Dynamics, 2013, 33(2):168-175.(in Chinese)
[6] 刘令波. 基于概率密度演化的非线性随机结构可靠度分析[D]. 大连:大连理工大学, 2013.LIU lingbo. Reliability Analysis of Nonlinear Stochastic Structures Based on Probability Density Evolution[D]. Dalian: Dalian University of Technology, 2013. (in Chinese)
[7] 梅真, 郭子雄, 高毅超. 基于模型结构振动台试验的概率密度演化方法验证[J]. 工程力学, 2017, 34(3): 54-61.MEI Zhen, GUO Zixiong, GAO Yichao. Validation of the probability density evolution method based on shaking table tests of a model structure [J]. Engineering Mechanics, 2017, 34(3): 54-61. (in Chinese)
[8] 李杰. 随机结构系统-分析与建模[M]. 北京: 科学出版社, 1996.LI Jie. Stochastic structure system-analysis and modeling[M]. Beijing: Science Press, 1996. (in Chinese)
[9] 朱玉华, 庄文娟, 黄海荣. 铅芯橡胶隔震支座水平刚度影响因素数值分析[J]. 结构工程师, 2009, 25(6): 66-71.ZHU Yuhua, ZHUANG Wenjuan, HUANG Hairong. Simulation analysis on effects of horizontal stiffness in lead-rubber bearings [J]. Structural Engineers, 2009, 25(6):66-71. (in Chinese)
[10] 艾方亮, 朱玉华, 任祥香. 不同尺寸铅芯橡胶隔震支座力学性能的有限元分析[J]. 结构工程师, 2016, 32(6): 74-79.AI Fangliang, ZHU Yuhua, REN Xiangxiang. FEA study on mechanical properties of lead-rubber bearings with different diameters [J]. Structural Engineers, 2016, 32(6):74-79.(in Chinese)
[11] 王建强, 辛伟, 李政, 等. 铅芯橡胶支座剪切性能影响因素分析[J]. 世界地震工程, 2014(3): 77-81.WANG Jianqiang, XIN Wei, LI Zheng, et al. Influence factor on shear properties of lead-rubber bearings [J]. World Earthquake Engineering, 2014(3):77-81.(in Chinese)
[12] 董玉勇, 陆飞, 张富有. 天然叠层橡胶支座水平刚度的概率统计分析[J]. 科学技术与工程, 2013, 13(11): 3158-3161.DONG Yuyong, LU Fei, ZHANG Fuyou. Study on characteristics of probability and statistics of rubber isolation bearing’s horizontal stiffness[J]. Science Technology and Engineering, 2013, 13(11):3158-3161.(in Chinese)
[13] Ahmadipour M, Alam M S. Sensitivity analysis on mechanical characteristics of lead-core steel-reinforced elastomeric bearings under cyclic loading[J]. Engineering Structures, 2017, 140: 39-50.
[14] 薛彦涛, 常兆中, 高杰. 隔震建筑设计指南[M]. 北京: 中国建筑工业出版社, 2016.XUE Yantao, CHANG Zhaozhong, GAO Jie. Designin guide for isolated buildings. Beijing: China Building Industry Press, 2016. (in Chinese)
[15] Chen J, Yang J, Li J. A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters[J]. Structural Safety, 2016, 59: 20-31.
[16] 陈建兵, 李杰. 随机结构动力可靠度分析的极值概率密度方法[J]. 地震工程与工程振动, 2004, 24(6): 39-44.CHEN Jianbing, LI Jie. The extreme value probability density function based method for dynamic reliability assessment of stochastic structures[J]. Earthquake Engineering and Engineering Dynamics, 2004, 24(6):39-44. (in Chinese)Uncertainty of equivalent horizontal stiffness of lead-rubber bearings based on probability density evolution method XUE Bin, ZHU Yuhua, HE Yi, et al.(145)Study on residual column drift rate collapse criteria of continuous girder bridge based on IDA CAI Xiaoyu, TIAN Shizhu(153)