高耸结构风振响应和风振疲劳研究
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摘要
高耸结构是一种特殊的结构形式,具有高度高、重量轻、刚度小、外形细长等特点,广泛应用于电力、通讯、广播电视等领域。高耸结构的外形特征决定了风荷载是其控制荷载,随着需求的提高和技术的进步,高耸结构日益向着更高、更轻、更柔的方向发展,使得对风荷载的敏感性进一步增强。
为了研究高耸结构在强风作用下的振动特性,本文对一自立式单杆输电塔进行了风洞试验研究。根据相似原理设计制作了气弹模型,在均匀流场中测定了模型的气动力系数,在风洞中模拟了大气边界层流场,在紊流流场中测定了模型振动响应,并将试验结果换算到实物,作为设计和计算的依据。
采用谐波叠加法模拟了脉动风速时程样本,在时域内计算了结构的顺风向动力响应。在频域内分别采用阵风因子法和荷载组合法计算了顺风向等效静力风荷载,并与我国规范规定的风振系数法进行了比较。考虑了风与结构耦合作用的影响,计算了结构的气动阻尼力。用随机振动方法计算了结构的横风向响应。将计算结果和风洞试验结果进行了比较和分析。
用基于疲劳累积损伤理论的S-N曲线法分析了高耸结构的风振疲劳问题。在时域内用雨流法统计了应力时程的幅值分布。在频域内分别用等效应力法和等效窄带法计算了累积损伤。在等效窄带法的基础上,通过将响应的背景分量和共振分量分开考虑,提出了一种新的改进算法,避免了计算应力谱的复杂计算。通过对计算结果的比较,证明了该方法的可行性。
研究了将疲劳裂纹扩展理论应用于风振疲劳问题。考虑平均风速的分布的影响,建立了随机荷载作用下的疲劳裂纹扩展模型。用零记忆非线性变换法模拟了满足Weibull分布和一定相关性的平均风速时间样本,计算了结构主裂纹扩展的时间样本,根据Monte-Carlo方法得出了给定时间的裂纹尺寸分布。推导了二次矩近似法的计算公式,用对数正态模型模拟了裂纹尺寸和到达时间的分布。计算了给定时间的破坏概率。分析了影响裂纹扩展的几个主要因素。
High-rise structure is somewhat different from others because of being high, light, soft and slim. It has been widely used in some related fields such as power transmission, communication , broadcasting and television system. Due to its characteristic of shape, the dominating load of high-rise structure is wind load. With the growth of demand and progress of technique, it has been developed to be much higher, lighter and softer which increases its sensitivity to wind load.For the purpose of studying the vibration characteristics of high-rise structure under high wind speed, a model of single-rod transmission tower was tested in wind tunnel. The aerodynamic model was designed and manufactured with similar principle. The boundary layer was simulated in wind tunnel. The aerodynamic force coefficients in laminar flow and the dynamic response in turbulence flow were measured in the experiment. The results were converted to the real structure.The time series of turbulent wind velocity were simulated by wave superposition method for numerical calculation. The along-wind response was calculated in time domain. The equivalent static wind force was calculated by gust response factor method and load combination method respectively. The result was compared with that of the dynamic wind coefficient method. The infuence of coupling effect was taken into account and aerodynamic damping force was calculated. What's more, the across-wind response was analized by random vibration method. The results were compared with that of the wind tunnel test.Wind-induced fatigue of high-rise structure was analysed by means of S-N curve method which was based on accumulated fatigue damage theory. The distribution of stress amplitude was accounted by rain-flow method in time domain. The accumulated fatigue damage was calculated in frequency domain by equivalent stress method and equivalent narrow band method respectively. On the basis of equivalent narrow band method, a new method was proposed by dividing the wind-induced stress into background part and resonant part, which avoid complexity of calculating stress spectrum. The feasibility of this method was proved by comparing its result with that of other methods.In this essay, the application of fatigue crack growth theory to wind-induced fatigue was also studied. Taking the distribution of mean wind velocity into account, the random crack growth model under variable amplitude load was established. The time series of mean wind velocity with given Weibull distribution and time related funtion were simulated by zero-memory nonlinearity method. The sample of crack growth was calculated. The statistical quantities were gained by Monte-Carlo method. The equations of second-order moment method were infered. The distribution of crack length and reached time was approximated by lognormal model. The destruction probability was calculated. Some factors which influenced the crack growth were analysed at the end.
为了研究高耸结构在强风作用下的振动特性,本文对一自立式单杆输电塔进行了风洞试验研究。根据相似原理设计制作了气弹模型,在均匀流场中测定了模型的气动力系数,在风洞中模拟了大气边界层流场,在紊流流场中测定了模型振动响应,并将试验结果换算到实物,作为设计和计算的依据。
采用谐波叠加法模拟了脉动风速时程样本,在时域内计算了结构的顺风向动力响应。在频域内分别采用阵风因子法和荷载组合法计算了顺风向等效静力风荷载,并与我国规范规定的风振系数法进行了比较。考虑了风与结构耦合作用的影响,计算了结构的气动阻尼力。用随机振动方法计算了结构的横风向响应。将计算结果和风洞试验结果进行了比较和分析。
用基于疲劳累积损伤理论的S-N曲线法分析了高耸结构的风振疲劳问题。在时域内用雨流法统计了应力时程的幅值分布。在频域内分别用等效应力法和等效窄带法计算了累积损伤。在等效窄带法的基础上,通过将响应的背景分量和共振分量分开考虑,提出了一种新的改进算法,避免了计算应力谱的复杂计算。通过对计算结果的比较,证明了该方法的可行性。
研究了将疲劳裂纹扩展理论应用于风振疲劳问题。考虑平均风速的分布的影响,建立了随机荷载作用下的疲劳裂纹扩展模型。用零记忆非线性变换法模拟了满足Weibull分布和一定相关性的平均风速时间样本,计算了结构主裂纹扩展的时间样本,根据Monte-Carlo方法得出了给定时间的裂纹尺寸分布。推导了二次矩近似法的计算公式,用对数正态模型模拟了裂纹尺寸和到达时间的分布。计算了给定时间的破坏概率。分析了影响裂纹扩展的几个主要因素。
High-rise structure is somewhat different from others because of being high, light, soft and slim. It has been widely used in some related fields such as power transmission, communication , broadcasting and television system. Due to its characteristic of shape, the dominating load of high-rise structure is wind load. With the growth of demand and progress of technique, it has been developed to be much higher, lighter and softer which increases its sensitivity to wind load.For the purpose of studying the vibration characteristics of high-rise structure under high wind speed, a model of single-rod transmission tower was tested in wind tunnel. The aerodynamic model was designed and manufactured with similar principle. The boundary layer was simulated in wind tunnel. The aerodynamic force coefficients in laminar flow and the dynamic response in turbulence flow were measured in the experiment. The results were converted to the real structure.The time series of turbulent wind velocity were simulated by wave superposition method for numerical calculation. The along-wind response was calculated in time domain. The equivalent static wind force was calculated by gust response factor method and load combination method respectively. The result was compared with that of the dynamic wind coefficient method. The infuence of coupling effect was taken into account and aerodynamic damping force was calculated. What's more, the across-wind response was analized by random vibration method. The results were compared with that of the wind tunnel test.Wind-induced fatigue of high-rise structure was analysed by means of S-N curve method which was based on accumulated fatigue damage theory. The distribution of stress amplitude was accounted by rain-flow method in time domain. The accumulated fatigue damage was calculated in frequency domain by equivalent stress method and equivalent narrow band method respectively. On the basis of equivalent narrow band method, a new method was proposed by dividing the wind-induced stress into background part and resonant part, which avoid complexity of calculating stress spectrum. The feasibility of this method was proved by comparing its result with that of other methods.In this essay, the application of fatigue crack growth theory to wind-induced fatigue was also studied. Taking the distribution of mean wind velocity into account, the random crack growth model under variable amplitude load was established. The time series of mean wind velocity with given Weibull distribution and time related funtion were simulated by zero-memory nonlinearity method. The sample of crack growth was calculated. The statistical quantities were gained by Monte-Carlo method. The equations of second-order moment method were infered. The distribution of crack length and reached time was approximated by lognormal model. The destruction probability was calculated. Some factors which influenced the crack growth were analysed at the end.
引文
[1] 范学伟等,工程结构的风灾破坏和抗风设计,中国安全科学学报,2001,11:73-76.
[2] 吕升亮等,亳州市电视铁塔倒塌事故的气象原因,气象,2001,27:52-54.
[3] 舒兴平等,某铁塔倒塌的事故分析,湖南大学学报,2004,31:56-58.
[4] 黄本才,结构抗风分析原理及应用,同济大学出版社,2001.
[5] 刘尚培等译,风对结构的作用——风工程导论,同济大学出版社,1992.
[6] 日本建议,AIJ recommendations for loads on building, 1996.
[7] Vickery B J, Lift or across-wind response of tapered stacks, ASCE, 98(ST1): 1-20.
[8] Solari G, Mathematical model to predict 3-D wind loading on buildings, Journal of engineering mechanics. 1985, 111, 21-29.
[9] 王肇民,高耸结构的发展与展望,特种结构,2000,1:4-7.
[10] Davenport A G, The application of statistical concepts to the wind loading of structures, Proc. Inst. Civ. Eng, 1961, 19: 419-427.
[11] Davenport A G, The response of slender, link-like structures to a gust wind, Proc. Inst. Civ. Eng, 1962, 23: 389-409.
[12] Davenport A G, Gust loading factors, Journal of the structural division, ASCE, 1967, 93: 11-34.
[13] Vellozzi J, Cohen E, Gust response factors, Journal of structures division, ASCE, 1968, 94: 295-313.
[14] Vickery B J, On the reliability of gust loading factors, Proceedings of the technicians meet concerning wind loads on buildings and structures, Washington D C, Nat Bur standards, 1970.
[15] Simiu E, Equivalent static wind loads for tall buildings design, Journal of structures division, ASCE, 1976, 102: 19-37
[16] Simiu E, Revised procedure for estimating alongwind response, Journal of structures division, ASCE, 1980, 106: 1-10.
[17] Solari G, Alongwind response estimation: closed-form solution, Journal of structures, Div, ASCE, 1982, 108: 225-244.
[18] Solari G, Analytical estimation of the alongwind response of structures, Journal of wind engineering and industrial aerodynamics, 1983, 14: 467-477.
[19] Kasperski M, Extreme wind load distributions for linear and nonlinear design, Engineering structures, 1992, 14: 27-34.
[20] Kasperski M, Niemann H J, The LRC method-a general method for estimating unfavourable wind load distributions for linear and nonlinear structural behaviour, Journal of wind engineering and industrial aerodynamics, 1992, 41-44: 1753-1763.
[21] Holmes J D, Along-wind response of lattice towers: part Ⅰ: derivation of expressions for gust response factors, Engineering structures, 1994,16:287-292.
[22] Holmes J D, Along-wind response of lattice towers: part Ⅲ: effective load distributions, Engineering structures, 1996, 18: 489-494.
[23] Piccardo G, Solari G. A refined model for calculating 3-D equivalent static wind forces on structures, Journal of wind engineering and industrial aerodynamics, 1996, 65: 21-30.
[24] Solari G, Mathematical model to predict 3-D wind loading on buildings, Journal of engineering mechanics, ASCE, 1985, 111: 254-276.
[25] Piccardo G, Solari G. Closed form prediction of 3-D wind-excited response of slender structures, Journal of wind engineering and industrial aerodynamics, 1998, 74-76: 697-708.
[26] Piccardo G, Solar G, 3-D wind-excited response of slender structures: closed form solution, Journal of structure engineering, ASCE, 2000, 126: 936-943.
[27] 蒋洪平,张相庭,变截面高耸结构的横向风振研究,振动与冲击,1994,1:46-54.
[28] 徐幼麟,张相庭,高耸结构风振响应的准静态效应,建筑结构学报,1991,12:61-69.
[29] 蒋洪平,张相庭,高耸结构的耦联阵风响应,应用力学学报,1993,10:65-74.
[30] 楼文娟,孙炳楠,高耸格构式结构风振数值分析及风洞试验,振动工程学报,1996,9:318-322.
[31] 楼文娟,孙炳楠,高耸塔架横风向动力风效应,土木工程学报,1999,32:67-71.
[32] 楼文娟,孙炳楠,风与结构的耦合作用及风振响应分析,工程力学,2000,17:16-22.
[33] 王肇民,朱照容,上海电视塔用TMD进行结构风振控制的风洞试验研究,特种结构,1994,11:14-17.
[34] 李树逊,王肇民,桅杆结构在模拟风荷载下的非线性动力分析,建筑结构,1999,9:44-46.
[35] Crandall S H, Mark W D, Random vibration in mechanical systems, New York, Academic press, 1963.
[36] Lutes C D, Corazao M, Hu S J, Zimmerman J, Stochastic fatigue damage accumulation, Journal of structure engineering, 1984, 110: 2585-2601.
[37] Jiao G, Moan T, Probabilistic analysis of fatigue due to Gaussian load processes, Probabilistic engineering mechanics, 1990, 5: 76-83.
[38] Winterstein S R, Non-linear vibration models for extremes and fatigue, Journal of engineering mechanics, ASCE,1986,114:1772-1790.
[39] Miles J W, On the structural fatigue under random loading, J. Aeronaut. Sci, 1954, 21.
[40] Bolotin V V, About life estimation at stationary random loads, Mashinostroenije, Moscow, 1959.
[41] Peil, Fatigue of high and slender structures under wind load, Aspects in moden computational structural analysis, 1997.
[42] Huang X, Hancock. J W, A reliability analysis of fatigue crack growth under random loading, Fatigue Fract Eng Mater Struct, 1989, 12: 247-258.
[43] Chaudhury G K, Dover W, Fatigue analysis of offshore platforms subject to sea wave loading, International journal of fatigue, 1985, 7: 13-19.
[44] Chow C L, Li D L, An analytical solution for fast fatigue assessment under wide-band random loading, International journal of fatigue, 1991, 5: 395-404.
[45] Wirsching P H, Fatigue under wide band random stresses, Journal of the structural division, 1980, 106: 1593-1607.
[46] Holmes J D, Fatigue life under along-wind loading: closed-form solutions, Engineering structures, 2002, 24: 109-114.
[47] Robertson A P, Holmes J D, Smith B W, Verification of closed-form solutions of fatigue life under along-wind loading, Engineering structures, 2004, 26: 1381-1387.
[48] 王之宏,桅杆结构的风振疲劳分析,特种结构,1994,11:3-8.
[49] 屠海明,邓洪洲,基于频域的桅杆结构风振疲劳分析,特种结构,1999,15:34-36.
[50] 欧进萍,叶骏,结构风振的概率疲劳累积损伤,振动工程学报,1993,6:164-169.
[51] 邓洪洲,温应龙,何鹏飞,格构式桅杆顺风向风振疲劳可靠性分析,特种结构,2004,21:31-35.
[52] Paris P C, Gomez M P, Andrson W E, A rational analytic theory of fatigue, The trend in engineering, 1961, 13: 9-14.
[53] Dolinski K, Fatigue crack growth with retardation under stationary stochastic loading, Engineering fracture mechanics, 1987, 27: 279-290.
[54] Schijve J, Fatigue predictions and scatter, Fatigue fracture and engineering material structures, 1994, 17: 381-396.
[55] Dolinski K, Fomulation of a stochastic model of fatigue crack growth, Fracture engineering of material structures, 1993,16:1007-1019.
[56] Bogdanoff J L, Kozin F, Probabilistic models of cumulative damage, Wiely, New York, 1985.
[57] Bogdanoff J L, Kozin F, Probabilistic models of fatigue crack growth-Ⅱ, Engineering fracture mechanics, 1984, 20: 255-270.
[58] Lin Y K, Yang J N, A stochastic theory of fatigue crack propagation, AIAA, 1985, 23: 117-124.
[59] Lin Y K, Yang J N, On statistical moments of fatigue crack propagation, Engineering fracture mechanics, 1983, 18: 243-256.
[60] Dominguez J, Zapatero J, Moreno B, A statistical model for fatigue crack growth under random loads including retardation effects, Engineering fracture mechanics, 1999, 62: 351-369.
[61] Provan J W主编,概率断裂力学和可靠性,航空工业出版社,1989.
[2] 吕升亮等,亳州市电视铁塔倒塌事故的气象原因,气象,2001,27:52-54.
[3] 舒兴平等,某铁塔倒塌的事故分析,湖南大学学报,2004,31:56-58.
[4] 黄本才,结构抗风分析原理及应用,同济大学出版社,2001.
[5] 刘尚培等译,风对结构的作用——风工程导论,同济大学出版社,1992.
[6] 日本建议,AIJ recommendations for loads on building, 1996.
[7] Vickery B J, Lift or across-wind response of tapered stacks, ASCE, 98(ST1): 1-20.
[8] Solari G, Mathematical model to predict 3-D wind loading on buildings, Journal of engineering mechanics. 1985, 111, 21-29.
[9] 王肇民,高耸结构的发展与展望,特种结构,2000,1:4-7.
[10] Davenport A G, The application of statistical concepts to the wind loading of structures, Proc. Inst. Civ. Eng, 1961, 19: 419-427.
[11] Davenport A G, The response of slender, link-like structures to a gust wind, Proc. Inst. Civ. Eng, 1962, 23: 389-409.
[12] Davenport A G, Gust loading factors, Journal of the structural division, ASCE, 1967, 93: 11-34.
[13] Vellozzi J, Cohen E, Gust response factors, Journal of structures division, ASCE, 1968, 94: 295-313.
[14] Vickery B J, On the reliability of gust loading factors, Proceedings of the technicians meet concerning wind loads on buildings and structures, Washington D C, Nat Bur standards, 1970.
[15] Simiu E, Equivalent static wind loads for tall buildings design, Journal of structures division, ASCE, 1976, 102: 19-37
[16] Simiu E, Revised procedure for estimating alongwind response, Journal of structures division, ASCE, 1980, 106: 1-10.
[17] Solari G, Alongwind response estimation: closed-form solution, Journal of structures, Div, ASCE, 1982, 108: 225-244.
[18] Solari G, Analytical estimation of the alongwind response of structures, Journal of wind engineering and industrial aerodynamics, 1983, 14: 467-477.
[19] Kasperski M, Extreme wind load distributions for linear and nonlinear design, Engineering structures, 1992, 14: 27-34.
[20] Kasperski M, Niemann H J, The LRC method-a general method for estimating unfavourable wind load distributions for linear and nonlinear structural behaviour, Journal of wind engineering and industrial aerodynamics, 1992, 41-44: 1753-1763.
[21] Holmes J D, Along-wind response of lattice towers: part Ⅰ: derivation of expressions for gust response factors, Engineering structures, 1994,16:287-292.
[22] Holmes J D, Along-wind response of lattice towers: part Ⅲ: effective load distributions, Engineering structures, 1996, 18: 489-494.
[23] Piccardo G, Solari G. A refined model for calculating 3-D equivalent static wind forces on structures, Journal of wind engineering and industrial aerodynamics, 1996, 65: 21-30.
[24] Solari G, Mathematical model to predict 3-D wind loading on buildings, Journal of engineering mechanics, ASCE, 1985, 111: 254-276.
[25] Piccardo G, Solari G. Closed form prediction of 3-D wind-excited response of slender structures, Journal of wind engineering and industrial aerodynamics, 1998, 74-76: 697-708.
[26] Piccardo G, Solar G, 3-D wind-excited response of slender structures: closed form solution, Journal of structure engineering, ASCE, 2000, 126: 936-943.
[27] 蒋洪平,张相庭,变截面高耸结构的横向风振研究,振动与冲击,1994,1:46-54.
[28] 徐幼麟,张相庭,高耸结构风振响应的准静态效应,建筑结构学报,1991,12:61-69.
[29] 蒋洪平,张相庭,高耸结构的耦联阵风响应,应用力学学报,1993,10:65-74.
[30] 楼文娟,孙炳楠,高耸格构式结构风振数值分析及风洞试验,振动工程学报,1996,9:318-322.
[31] 楼文娟,孙炳楠,高耸塔架横风向动力风效应,土木工程学报,1999,32:67-71.
[32] 楼文娟,孙炳楠,风与结构的耦合作用及风振响应分析,工程力学,2000,17:16-22.
[33] 王肇民,朱照容,上海电视塔用TMD进行结构风振控制的风洞试验研究,特种结构,1994,11:14-17.
[34] 李树逊,王肇民,桅杆结构在模拟风荷载下的非线性动力分析,建筑结构,1999,9:44-46.
[35] Crandall S H, Mark W D, Random vibration in mechanical systems, New York, Academic press, 1963.
[36] Lutes C D, Corazao M, Hu S J, Zimmerman J, Stochastic fatigue damage accumulation, Journal of structure engineering, 1984, 110: 2585-2601.
[37] Jiao G, Moan T, Probabilistic analysis of fatigue due to Gaussian load processes, Probabilistic engineering mechanics, 1990, 5: 76-83.
[38] Winterstein S R, Non-linear vibration models for extremes and fatigue, Journal of engineering mechanics, ASCE,1986,114:1772-1790.
[39] Miles J W, On the structural fatigue under random loading, J. Aeronaut. Sci, 1954, 21.
[40] Bolotin V V, About life estimation at stationary random loads, Mashinostroenije, Moscow, 1959.
[41] Peil, Fatigue of high and slender structures under wind load, Aspects in moden computational structural analysis, 1997.
[42] Huang X, Hancock. J W, A reliability analysis of fatigue crack growth under random loading, Fatigue Fract Eng Mater Struct, 1989, 12: 247-258.
[43] Chaudhury G K, Dover W, Fatigue analysis of offshore platforms subject to sea wave loading, International journal of fatigue, 1985, 7: 13-19.
[44] Chow C L, Li D L, An analytical solution for fast fatigue assessment under wide-band random loading, International journal of fatigue, 1991, 5: 395-404.
[45] Wirsching P H, Fatigue under wide band random stresses, Journal of the structural division, 1980, 106: 1593-1607.
[46] Holmes J D, Fatigue life under along-wind loading: closed-form solutions, Engineering structures, 2002, 24: 109-114.
[47] Robertson A P, Holmes J D, Smith B W, Verification of closed-form solutions of fatigue life under along-wind loading, Engineering structures, 2004, 26: 1381-1387.
[48] 王之宏,桅杆结构的风振疲劳分析,特种结构,1994,11:3-8.
[49] 屠海明,邓洪洲,基于频域的桅杆结构风振疲劳分析,特种结构,1999,15:34-36.
[50] 欧进萍,叶骏,结构风振的概率疲劳累积损伤,振动工程学报,1993,6:164-169.
[51] 邓洪洲,温应龙,何鹏飞,格构式桅杆顺风向风振疲劳可靠性分析,特种结构,2004,21:31-35.
[52] Paris P C, Gomez M P, Andrson W E, A rational analytic theory of fatigue, The trend in engineering, 1961, 13: 9-14.
[53] Dolinski K, Fatigue crack growth with retardation under stationary stochastic loading, Engineering fracture mechanics, 1987, 27: 279-290.
[54] Schijve J, Fatigue predictions and scatter, Fatigue fracture and engineering material structures, 1994, 17: 381-396.
[55] Dolinski K, Fomulation of a stochastic model of fatigue crack growth, Fracture engineering of material structures, 1993,16:1007-1019.
[56] Bogdanoff J L, Kozin F, Probabilistic models of cumulative damage, Wiely, New York, 1985.
[57] Bogdanoff J L, Kozin F, Probabilistic models of fatigue crack growth-Ⅱ, Engineering fracture mechanics, 1984, 20: 255-270.
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