传统反应谱CQC法研究与改进
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摘要
工程抗震设计的首要任务是确定结构的地震作用及其效应,以此作为设计校核的依据。目前,反应谱CQC法是我国和世界多数国家抗震设计规范所推荐的计算地震作用及其效应的首选方法。地震地面运动实际上是取决于地震规模、震源机制、传播路径和场地条件等许多复杂因素的随机过程,结构的地震响应也是一个随机过程,理论上采用随机振动分析法来进行结构抗震计算比较合理。由于随机振动分析法的计算复杂性和高昂的计算成本成为其通向工程应用的瓶颈,工程师们为了绕过这些困难,不得不寻找能够大幅提高计算效率又能保证计算精度的近似方法,于是提出了反应谱CQC法。工程界普遍认为,应用现行反应谱CQC法(本文以下称为传统反应谱CQC法)计算结构的地震作用及其效应,既能保证计算精度,又能节约计算成本。但在实际工程中发现,某些结构的传统反应谱CQC法计算结果比实际偏小较多,有的不能很好地解释某些震害现象,有的与模型试验结果明显不符。因此,本文围绕改进传统反应谱CQC法计算结果的准确度这一目标,根据随机振动分析理论和反应谱理论对反应谱CQC法进行了深入研究,主要取得了以下成果;
1、在不增加计算难度和计算过程复杂性的前提下,提出了有效提高计算结果准确度的改进反应谱CQC法。利用国际著名商用软件MSC.Nastran对实际工程结构进行随机振动分析和时程分析,分别将计算结果与传统反应谱CQC法和改进反应谱CQC法的计算结果进行分析比较,验证了传统反应谱CQC法的不合理性和改进反应谱CQC法的正确性;
2、将规范加速度反应谱转换为当量功率谱密度,分别按白噪声假定和当量功率谱密度计算模态相关系数,采用MSC.Nastran和自编的程序分别应用传统反应谱CQC法和改进反应谱CQC法计算实际工程的地震作用效应,验证了将实际地震动简化为白噪声具有充分的合理性,为改进反应谱CQC法提供了实用可行性;
3、结构随机振动分析法的计算结果显示,在应用反应谱CQC法计算复杂结构的地震作用效应时,被截断高频模态的影响不可忽视,尤其对底部楼层的竖向结构构件更是如此。为此,本文又提出了考虑被截断高频模态影响的改进改进反应谱CQC法,以进一步提高计算结果的准确度;
4、反应谱CQC法计算结果的准确度还与参与组合的模态个数密切相关,目前广为应用的确定合理组合模态个数的方法是质量参与系数法。本文指出了质量参与系数法存在的不足,提出了有效且简单易用的频率控制法,作为质量参与系数法的补充,可以进一步提高反应谱CQC法计算结果的准确度;
The most important task of anti-seismic design of structures is to determine the earthquake action and its effect which act as an important basis of design and verification. At the present time, the response spectrum CQC method is the most recommended method by code for anti-seismic design of structures in China and most other countries. As the ground action is in fact a random process which depending on quake scale, quake mechanism, propagation path and site condition, etc. it is reasonable to perform the anti-seismic design with random vibration analysis method in theory. The complex calculation and expensive cost of random vibration analysis method make it be the bottleneck of its wide application. In order to bypass the application difficulties of random vibration analysis method, engineers have no choice but to explore other methods which can improve calculation efficiency significantly and can ensure enough accuracy, hence the response spectrum CQC method is introduced. It is regarded by engineering world that the earthquake and its effect obtained with traditional response spectrum CQC method can ensure enough accuracy as well as less calculation cost. But when be putting into practice, the results obtained with traditional response spectrum CQC method may be much less than the real ones, and some time they can't explain the damage causes by earthquake, and some time they don't agree with the results of model test. In this paper, all works are centered about the object to improve the accuracy of traditional response spectrum CQC method, and intensive researches are performed according to random vibration theory and response spectrum theory. The following are some primary achievements:
1. The improved response spectrum CQC method which features good accuracy is introduced, while the improved method doesn't increase calculation difficulties and complexities. By means of calculating with well-known commercial program MSC.Nastran and comparing results of traditional response spectrum method and improved response spectrum method with results of random vibration analysis method and time history analysis method respectively, it comes to conclude that the improved response spectrum method is more reasonable while the traditional response spectrum method is not satisfactory.
2. The acceleration response spectrum defined in state design code is transformed to consistent power spectrum density. Using the white noise assumption of ground action and the consistent power spectrum density respectively, modal correlation coefficient is calculated, and then using results from modal analysis with MSC.Nastran, calculation is performed with traditional response spectrum CQC method and improved response spectrum CQC method and self-coded program. It's proved that the white noise assumption of ground action is fully reasonable after comparing above results each other, so it is possible for the improved response spectrum CQC method to be widely applied in engineering.
3. Results obtained with random vibration analysis method show that when calculating earthquake action and its effect of structure components of complicated buildings with response spectrum CQC method, the influence of truncated high frequency mode can not be neglected, especially at location near bottom. Therefore, in order to get more accurate results, it is suggested that the calculation be performed with improved response spectrum CQC method and the influence of truncated high frequency mode also be included.
4. The accuracy degree of results obtained with response spectrum CQC method also depends on number of combined modes to a great extent. At present time, the widely applied method to determine reasonable number of combined modes is mass participation ratio method. In this paper, deficiencies of mass participation ratio method are analyzed and efficient frequency control method which can act as a good supplement is introduced at the same time. Compared with mass participation ratio method, the frequency control method can efficiently increase accuracy of results obtained with response spectrum CQC method.
1、在不增加计算难度和计算过程复杂性的前提下,提出了有效提高计算结果准确度的改进反应谱CQC法。利用国际著名商用软件MSC.Nastran对实际工程结构进行随机振动分析和时程分析,分别将计算结果与传统反应谱CQC法和改进反应谱CQC法的计算结果进行分析比较,验证了传统反应谱CQC法的不合理性和改进反应谱CQC法的正确性;
2、将规范加速度反应谱转换为当量功率谱密度,分别按白噪声假定和当量功率谱密度计算模态相关系数,采用MSC.Nastran和自编的程序分别应用传统反应谱CQC法和改进反应谱CQC法计算实际工程的地震作用效应,验证了将实际地震动简化为白噪声具有充分的合理性,为改进反应谱CQC法提供了实用可行性;
3、结构随机振动分析法的计算结果显示,在应用反应谱CQC法计算复杂结构的地震作用效应时,被截断高频模态的影响不可忽视,尤其对底部楼层的竖向结构构件更是如此。为此,本文又提出了考虑被截断高频模态影响的改进改进反应谱CQC法,以进一步提高计算结果的准确度;
4、反应谱CQC法计算结果的准确度还与参与组合的模态个数密切相关,目前广为应用的确定合理组合模态个数的方法是质量参与系数法。本文指出了质量参与系数法存在的不足,提出了有效且简单易用的频率控制法,作为质量参与系数法的补充,可以进一步提高反应谱CQC法计算结果的准确度;
The most important task of anti-seismic design of structures is to determine the earthquake action and its effect which act as an important basis of design and verification. At the present time, the response spectrum CQC method is the most recommended method by code for anti-seismic design of structures in China and most other countries. As the ground action is in fact a random process which depending on quake scale, quake mechanism, propagation path and site condition, etc. it is reasonable to perform the anti-seismic design with random vibration analysis method in theory. The complex calculation and expensive cost of random vibration analysis method make it be the bottleneck of its wide application. In order to bypass the application difficulties of random vibration analysis method, engineers have no choice but to explore other methods which can improve calculation efficiency significantly and can ensure enough accuracy, hence the response spectrum CQC method is introduced. It is regarded by engineering world that the earthquake and its effect obtained with traditional response spectrum CQC method can ensure enough accuracy as well as less calculation cost. But when be putting into practice, the results obtained with traditional response spectrum CQC method may be much less than the real ones, and some time they can't explain the damage causes by earthquake, and some time they don't agree with the results of model test. In this paper, all works are centered about the object to improve the accuracy of traditional response spectrum CQC method, and intensive researches are performed according to random vibration theory and response spectrum theory. The following are some primary achievements:
1. The improved response spectrum CQC method which features good accuracy is introduced, while the improved method doesn't increase calculation difficulties and complexities. By means of calculating with well-known commercial program MSC.Nastran and comparing results of traditional response spectrum method and improved response spectrum method with results of random vibration analysis method and time history analysis method respectively, it comes to conclude that the improved response spectrum method is more reasonable while the traditional response spectrum method is not satisfactory.
2. The acceleration response spectrum defined in state design code is transformed to consistent power spectrum density. Using the white noise assumption of ground action and the consistent power spectrum density respectively, modal correlation coefficient is calculated, and then using results from modal analysis with MSC.Nastran, calculation is performed with traditional response spectrum CQC method and improved response spectrum CQC method and self-coded program. It's proved that the white noise assumption of ground action is fully reasonable after comparing above results each other, so it is possible for the improved response spectrum CQC method to be widely applied in engineering.
3. Results obtained with random vibration analysis method show that when calculating earthquake action and its effect of structure components of complicated buildings with response spectrum CQC method, the influence of truncated high frequency mode can not be neglected, especially at location near bottom. Therefore, in order to get more accurate results, it is suggested that the calculation be performed with improved response spectrum CQC method and the influence of truncated high frequency mode also be included.
4. The accuracy degree of results obtained with response spectrum CQC method also depends on number of combined modes to a great extent. At present time, the widely applied method to determine reasonable number of combined modes is mass participation ratio method. In this paper, deficiencies of mass participation ratio method are analyzed and efficient frequency control method which can act as a good supplement is introduced at the same time. Compared with mass participation ratio method, the frequency control method can efficiently increase accuracy of results obtained with response spectrum CQC method.
引文
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