大跨屋盖结构风致振动分析及等效静力风荷载研究
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摘要
大跨屋盖结构体型各异,且具有质量轻、柔度大、阻尼小、振型密集等一系列特点,其风荷载分布、风振响应分析及等效静力风荷载的计算都具有特殊性。本文通过随机振动理论分析、风洞动态测压试验和工程案例计算,给出了大跨屋盖结构抗风类型划分标准,提出了大跨屋盖结构风振响应和等效静力风荷载计算的SCQC法和CLRC法,并进行了多目标等效静力风荷载的研究。本文的主要研究内容如下：
1.大跨屋盖结构及其抗风分析方法回顾：对大跨屋盖结构的发展概况进行了总结,并对历年来大跨屋盖结构的风毁事件进行了回顾。在对大跨屋盖结构的表面风荷载、风振响应和等效静力风荷载研究现状进行系统总结和比较的基础上,指出了各种方法优缺点和适用条件。针对目前大跨屋盖结构抗风研究存在的不足和需要改进之处,引申出本文需要进行的研究工作。
2.大跨屋盖结构风洞动态测压试验：以一大跨屋盖结构动态测压风洞试验为例,介绍了风洞动态测压试验的基本原理和数据处理方法。对模型制作、测点布置、系统要求、试验安排以及风洞测压数据到实际结构风荷载的换算等一系列过程进行了较详细的介绍和分析。另一方面,由于频域分析需要将时程数据转换为功率谱的形式,文中给出了结构模态力谱的计算公式。
3.大跨屋盖结构抗风类型划分：考虑到大跨屋盖结构自身特性的差异、不同屋盖对风的敏感程度的差异、以及各种风振分析和等效静力风荷载计算方法的适用性,对大跨屋盖结构抗风类型进行了系统的划分。提出了保障率的概念,并根据大跨屋盖结构平均响应、脉动风背景响应和脉动风共振响应所占的比重,将大跨屋盖结构抗风类型划分为四类。进一步给出各分类的划分标准,指出每种类型适用的抗风分析方法,选择与之对应的抗风分析方法,可以同时兼顾效率和精度。
4.大跨屋盖结构考虑模态耦合效应的共振SCQC法：针对目前大跨屋盖结构考虑共振响应模态耦合效应计算方法的现状,本文提出一种简化的风振计算方法,称为简化CQC法(简称：SCQC法)。SCQC法考虑了各共振模态的耦合效应,具有较高的计算精度。本文推导了模态频响传递函数和模态力谱实部乘积和虚部乘积对响应方差贡献的计算公式,该公式不需要进行传统CQC法复杂的积分过程,进行简单的求和运算就能得到模态耦合项对响应方差的贡献,极大提高了计算效率,推导公式过程中所作的简化对于大跨屋盖结构也是合理的。
5.大跨屋盖结构风振响应和等效静力风荷载CLRC法：本文通过对动力方程的变换,得到广义恢复力向量,将其当作新的输入荷载,可将动力方程变为拟静力方程,进而可采用本文提出的一致LRC法(简称：CLRC法)进行风振响应和等效静力风荷载的求解。CLRC法可以与任何风振响应计算方法相适应,关键是获得广义恢复力协方差矩阵。当采用时域法时,得到结构的整体动态响应,可直接计算位移响应的协方差矩阵,进而得到广义恢复力的协方差矩阵；当采用频域法时,广义恢复力的协方差矩阵可以根据模态响应协方差矩阵计算得到。特别对于需要同时考虑背景分量和共振分量的结构,CLRC法中的三分量方法,考虑了模态耦合效应,其计算结构风振响应精度较高,与CQC方法误差非常小；同时,通过广义恢复力协方差矩阵的分别求解,在计算效率上远高于CQC方法。
6.大跨屋盖结构多目标等效静力风荷载方法：由于大跨屋盖多振型参与结构风振,结构响应往往不能同时到达极值。在单目标等效静力风荷载的作用下,仅仅等效目标的静力响应与动力响应极值相等,其他目标响应与实际动力响应极值常常相差较大。在分析以往多目标等效静风荷载研究的基础上,提出了一种新的多目标等效静力风荷载计算方法。该方法选择广义恢复力的本征模态作为构造多目标等效静力风荷载的基本向量,并引入约束方程组和权值因子,根据最小二乘法,可以得到这些基本向量的最优组合系数。该方法既解决了多目标等效静力风荷载问题,又保证了所得等效静力风荷载分布较为合理。
最后,对本文的主要研究成果进行了总结,并讨论了下一步需要进行的研究工作。
Long-span roof structures are composed of facilities of different structures and shapes, with the characteristics of light weight, large flexibility, small damping, closed natural frequencies and so on. Hence their wind load distribution, wind-induced vibration analysis and equivalent static wind loads are unique. In this article, based on the theory of random vibration, wind tunnel test and engineering projects, wind-resistant types classification criterion was given for long-span roof structures, also Simplified-CQC and Consistent-LRC methods were proposed for wind-induced vibration and equivalent static wind loads, finally universal equivalent static wind loads research was conducted. The main contents are as follows:
1. Long-span roof structures and their wind resistance analysis method were reviewed. Based on the systematical summary and comparison for surface wind loads, wind-induced vibration and equivalent static wind loads of the long-span roof structures, the advantages and disadvantages of each method and application requirements were pointed out. In view of deficiencies and improvement of the wind-resistant research, the needed research work was extended.
2. The wind tunnel dynamic pressure test of a long-span roof structure was taken as an example. The principle and data processing method for wind tunnel test were introduced. In addition, the structure modal force spectrum calculation formula was given to facilitate frequency domain analysis of structral respinses.
3. Wind-resistant types for long-span roof structures were classified systematically considering the differences of characteristics, the sensitivity to wind, and the wind vibration analysis. The concept of guarantee rate was defined, and according to the proportion of average response, background response and resonant response, wind-resistant types were classified into four kinds. For any type, the corresponding wind-resistant analysis method will be choosen, which can make a better compromise between the efficiency and accuracy.
4. The resonant SCQC method of long-span roof structures considering modal coupling effects was presented. The response variance calculation formula was given, which can consider the response variance contribution by modal coupling effects through simple summations instead of complex integration. Hence the calculation efficiency was greatly improved. Furthermore, the process of deducing the formula of simplified for long-span roof structures is reasonable, the calculation precision is also warranted.
5. The CLRC method for wind-induced vibration and equivalent static wind loads of long-span roof structures was presented. The CLRC method can be adapted to any wind vibration response calculation method, and the key is to get generalized recovery force covariance matrix. Especially for the need to simultaneously consider the background component and the resonant component structure, modal coupling effects were included in the CLRC method. At the same time, by solving the generalized recovery force covariance matrix respectively, thus the calculation efficiency is much higher than that of CQC method.
6. Based on the analysis of the past universal equivalent static wind loads, a new method of universal equivalent static wind loads was addressed. In this method, the generalized recovery force mode was selected as the basic vectors, and a set of constraint equations and weight factor was introduced. Using the least square method, optimal combination coefficient for the basic vector can be obtained. The method not only solves problems of the universal equivalent static wind loads, but also ensures that the equivalent static wind load distribution be more reasonable.
Finally, the main research results were summarized, and further research work that will be carried out was discussed.
1.大跨屋盖结构及其抗风分析方法回顾：对大跨屋盖结构的发展概况进行了总结,并对历年来大跨屋盖结构的风毁事件进行了回顾。在对大跨屋盖结构的表面风荷载、风振响应和等效静力风荷载研究现状进行系统总结和比较的基础上,指出了各种方法优缺点和适用条件。针对目前大跨屋盖结构抗风研究存在的不足和需要改进之处,引申出本文需要进行的研究工作。
2.大跨屋盖结构风洞动态测压试验：以一大跨屋盖结构动态测压风洞试验为例,介绍了风洞动态测压试验的基本原理和数据处理方法。对模型制作、测点布置、系统要求、试验安排以及风洞测压数据到实际结构风荷载的换算等一系列过程进行了较详细的介绍和分析。另一方面,由于频域分析需要将时程数据转换为功率谱的形式,文中给出了结构模态力谱的计算公式。
3.大跨屋盖结构抗风类型划分：考虑到大跨屋盖结构自身特性的差异、不同屋盖对风的敏感程度的差异、以及各种风振分析和等效静力风荷载计算方法的适用性,对大跨屋盖结构抗风类型进行了系统的划分。提出了保障率的概念,并根据大跨屋盖结构平均响应、脉动风背景响应和脉动风共振响应所占的比重,将大跨屋盖结构抗风类型划分为四类。进一步给出各分类的划分标准,指出每种类型适用的抗风分析方法,选择与之对应的抗风分析方法,可以同时兼顾效率和精度。
4.大跨屋盖结构考虑模态耦合效应的共振SCQC法：针对目前大跨屋盖结构考虑共振响应模态耦合效应计算方法的现状,本文提出一种简化的风振计算方法,称为简化CQC法(简称：SCQC法)。SCQC法考虑了各共振模态的耦合效应,具有较高的计算精度。本文推导了模态频响传递函数和模态力谱实部乘积和虚部乘积对响应方差贡献的计算公式,该公式不需要进行传统CQC法复杂的积分过程,进行简单的求和运算就能得到模态耦合项对响应方差的贡献,极大提高了计算效率,推导公式过程中所作的简化对于大跨屋盖结构也是合理的。
5.大跨屋盖结构风振响应和等效静力风荷载CLRC法：本文通过对动力方程的变换,得到广义恢复力向量,将其当作新的输入荷载,可将动力方程变为拟静力方程,进而可采用本文提出的一致LRC法(简称：CLRC法)进行风振响应和等效静力风荷载的求解。CLRC法可以与任何风振响应计算方法相适应,关键是获得广义恢复力协方差矩阵。当采用时域法时,得到结构的整体动态响应,可直接计算位移响应的协方差矩阵,进而得到广义恢复力的协方差矩阵；当采用频域法时,广义恢复力的协方差矩阵可以根据模态响应协方差矩阵计算得到。特别对于需要同时考虑背景分量和共振分量的结构,CLRC法中的三分量方法,考虑了模态耦合效应,其计算结构风振响应精度较高,与CQC方法误差非常小；同时,通过广义恢复力协方差矩阵的分别求解,在计算效率上远高于CQC方法。
6.大跨屋盖结构多目标等效静力风荷载方法：由于大跨屋盖多振型参与结构风振,结构响应往往不能同时到达极值。在单目标等效静力风荷载的作用下,仅仅等效目标的静力响应与动力响应极值相等,其他目标响应与实际动力响应极值常常相差较大。在分析以往多目标等效静风荷载研究的基础上,提出了一种新的多目标等效静力风荷载计算方法。该方法选择广义恢复力的本征模态作为构造多目标等效静力风荷载的基本向量,并引入约束方程组和权值因子,根据最小二乘法,可以得到这些基本向量的最优组合系数。该方法既解决了多目标等效静力风荷载问题,又保证了所得等效静力风荷载分布较为合理。
最后,对本文的主要研究成果进行了总结,并讨论了下一步需要进行的研究工作。
Long-span roof structures are composed of facilities of different structures and shapes, with the characteristics of light weight, large flexibility, small damping, closed natural frequencies and so on. Hence their wind load distribution, wind-induced vibration analysis and equivalent static wind loads are unique. In this article, based on the theory of random vibration, wind tunnel test and engineering projects, wind-resistant types classification criterion was given for long-span roof structures, also Simplified-CQC and Consistent-LRC methods were proposed for wind-induced vibration and equivalent static wind loads, finally universal equivalent static wind loads research was conducted. The main contents are as follows:
1. Long-span roof structures and their wind resistance analysis method were reviewed. Based on the systematical summary and comparison for surface wind loads, wind-induced vibration and equivalent static wind loads of the long-span roof structures, the advantages and disadvantages of each method and application requirements were pointed out. In view of deficiencies and improvement of the wind-resistant research, the needed research work was extended.
2. The wind tunnel dynamic pressure test of a long-span roof structure was taken as an example. The principle and data processing method for wind tunnel test were introduced. In addition, the structure modal force spectrum calculation formula was given to facilitate frequency domain analysis of structral respinses.
3. Wind-resistant types for long-span roof structures were classified systematically considering the differences of characteristics, the sensitivity to wind, and the wind vibration analysis. The concept of guarantee rate was defined, and according to the proportion of average response, background response and resonant response, wind-resistant types were classified into four kinds. For any type, the corresponding wind-resistant analysis method will be choosen, which can make a better compromise between the efficiency and accuracy.
4. The resonant SCQC method of long-span roof structures considering modal coupling effects was presented. The response variance calculation formula was given, which can consider the response variance contribution by modal coupling effects through simple summations instead of complex integration. Hence the calculation efficiency was greatly improved. Furthermore, the process of deducing the formula of simplified for long-span roof structures is reasonable, the calculation precision is also warranted.
5. The CLRC method for wind-induced vibration and equivalent static wind loads of long-span roof structures was presented. The CLRC method can be adapted to any wind vibration response calculation method, and the key is to get generalized recovery force covariance matrix. Especially for the need to simultaneously consider the background component and the resonant component structure, modal coupling effects were included in the CLRC method. At the same time, by solving the generalized recovery force covariance matrix respectively, thus the calculation efficiency is much higher than that of CQC method.
6. Based on the analysis of the past universal equivalent static wind loads, a new method of universal equivalent static wind loads was addressed. In this method, the generalized recovery force mode was selected as the basic vectors, and a set of constraint equations and weight factor was introduced. Using the least square method, optimal combination coefficient for the basic vector can be obtained. The method not only solves problems of the universal equivalent static wind loads, but also ensures that the equivalent static wind load distribution be more reasonable.
Finally, the main research results were summarized, and further research work that will be carried out was discussed.
引文
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