钢结构智能稳定控制的基本理论研究
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摘要
钢材具有良好的强度和延性，易于加工，施工方便，但杆系钢结构的稳定问题比较突出。而且结构或者构件一旦失稳破坏，则结构随即倒塌崩溃，发生灾难性工程事故，因此钢结构的稳定问题一直都是土木工程领域的研究热点之一。
智能材料具有自诊断、自调节、自恢复、自修复和智能驱动等功能，在土木工程中有着广阔的应用前景。例如，利用压电材料特殊的正、逆压电效应，即可研制开发高效可靠的压电智能传感器和压电智能驱动器，从而实现土木工程结构的智能振动控制、智能稳定控制或智能监测等。这是一个新型的研究方向，许多问题目前还处于研究的起步阶段。
本文提出了一种在普通钢构件中嵌入压电堆，形成智能主动控制元件，即主元杆件。这种杆件具有检测和驱动功能，若将其安装在结构中，则可实现对钢结构静力和动力稳定的主动控制。
基于上述思想，论文首先推导了嵌入压电堆杆件在静力作用下的稳定方程，考虑了非机电耦合与机电耦合两种情况，利用算例探讨了主元杆件中压电堆长度和出力对主元杆件稳定性的影响；然后采用同样的方法，进行了动力作用下主元杆件的稳定性分析，得出了简谐荷载下动力失稳的Mathieu—Hill方程。
其次，以计算模型为例，采用理论分析和有限元计算相结合的方法，进行了模型节点配重和结构主元杆件的优化布置分析，并通过对主元杆件中压电堆的4种嵌入方式的比较，探讨了主元杆件中压电堆嵌固位置和压电堆长度对结构稳定控制的影响规律，为经济合理地利用压电堆进行结构稳定控制提供了理论依据。
最后，采用有限元方法对模型结构进行了动力时程分析，主要计算了结构未设置主元杆件和设置主元杆件时的动力时程响应，得出了在不同地震动峰值加速度下结构的最大位移和特征节点的位移时程曲线。采用B—R动力失稳判别准则，研究了结构的动力失稳问题，并对两种情况的计算结果进行了对比，得出了设置主元杆件可以有效延缓结构动力失稳等一系列结论，为进一步深入研究提供参考。
Steel possesses a good ability of high strength and ductility, and is easy for processing and convenient for building; however, the stability of the skeleton steel structure becomes conspicuous. Moreover, once the stability break of the structure or its member occurs, the whole structure collapses instantly and incurs disastrous engineering accident. It follows therefore that the stability of the steel structure has been the research focus in civil engineering.
Smart material structures, with such functions as self-diagnose, self-tuning, self-recovery, self-repair and smart drive, enjoy wide application in civil engineering. For example, owing to its special positive and negative piezoelectric effects, the piezoelectric material can be developed into piezoelectric smart feeler unit and driver with high efficiency and reliance, thus achieving such functions as smart quiver control, smart stability control, smart monitoring, etc in civil engineering. This is a new research field, so at present, many problems are still in their initial stage.
This thesis advances a new method of embedding piezoelectric piles to the common steel structure to form the smart active control element in the structure, that is, the pivot element bar. And this element can check as well as drive, so it can actively control the stability in the steel structure or its member.
Based on the above considerations, first of all, the stability equation of the pivot element bar with piezoelectric piles embedded is deduced in both cases of static forces and dynamic forces, with both cases of non-mechanic-electric couple and mechanic-electric couple taken into considerations. Besides, the effect on the stability of the pivot element bar by the length and supply of the piezoelectric pile is demonstrated with calculations. Then, through the same procedures, the analysis of the stability of the pivot element bar is performed, and Mathieu-Hill Equation-the equation of dynamic stability break under the simple harmonic load is reached.
Secondly, with the model as the example, theoretical analysis and calculation by finite element software are used to reach the proper mass of the model node and to find the proper site of the pivot element bar. Through the analysis of the four methods of embedding piezoelectric piles to the pivot element bar, the most appropriately embedding position is found and the most appropriate length of the pile is also reached, thus supplying the theoretical basis in employing piezoelectric materials properly and economically.
At last, the dynamic time history analysis of the model is proceeded with the finite element analysis software. By analyzing and computing the dynamic time history response of the structure without piezoelectric piles embedded, the maximum displacement of the structure and the time curve of typical nodes are reached under various earthquake summits. And likewise, the dynamic time history response is analyzed and computed with piezoelectric piles embedded. And B-R guideline is used in judging the stability of structure. Then by comparing the results of the two cases, the thesis arrives at a natural conclusion that embedding the pivot element bar can delay the stability of the structure. Thus this thesis supplies the theoretical basis for specific jarring table experiments.
智能材料具有自诊断、自调节、自恢复、自修复和智能驱动等功能，在土木工程中有着广阔的应用前景。例如，利用压电材料特殊的正、逆压电效应，即可研制开发高效可靠的压电智能传感器和压电智能驱动器，从而实现土木工程结构的智能振动控制、智能稳定控制或智能监测等。这是一个新型的研究方向，许多问题目前还处于研究的起步阶段。
本文提出了一种在普通钢构件中嵌入压电堆，形成智能主动控制元件，即主元杆件。这种杆件具有检测和驱动功能，若将其安装在结构中，则可实现对钢结构静力和动力稳定的主动控制。
基于上述思想，论文首先推导了嵌入压电堆杆件在静力作用下的稳定方程，考虑了非机电耦合与机电耦合两种情况，利用算例探讨了主元杆件中压电堆长度和出力对主元杆件稳定性的影响；然后采用同样的方法，进行了动力作用下主元杆件的稳定性分析，得出了简谐荷载下动力失稳的Mathieu—Hill方程。
其次，以计算模型为例，采用理论分析和有限元计算相结合的方法，进行了模型节点配重和结构主元杆件的优化布置分析，并通过对主元杆件中压电堆的4种嵌入方式的比较，探讨了主元杆件中压电堆嵌固位置和压电堆长度对结构稳定控制的影响规律，为经济合理地利用压电堆进行结构稳定控制提供了理论依据。
最后，采用有限元方法对模型结构进行了动力时程分析，主要计算了结构未设置主元杆件和设置主元杆件时的动力时程响应，得出了在不同地震动峰值加速度下结构的最大位移和特征节点的位移时程曲线。采用B—R动力失稳判别准则，研究了结构的动力失稳问题，并对两种情况的计算结果进行了对比，得出了设置主元杆件可以有效延缓结构动力失稳等一系列结论，为进一步深入研究提供参考。
Steel possesses a good ability of high strength and ductility, and is easy for processing and convenient for building; however, the stability of the skeleton steel structure becomes conspicuous. Moreover, once the stability break of the structure or its member occurs, the whole structure collapses instantly and incurs disastrous engineering accident. It follows therefore that the stability of the steel structure has been the research focus in civil engineering.
Smart material structures, with such functions as self-diagnose, self-tuning, self-recovery, self-repair and smart drive, enjoy wide application in civil engineering. For example, owing to its special positive and negative piezoelectric effects, the piezoelectric material can be developed into piezoelectric smart feeler unit and driver with high efficiency and reliance, thus achieving such functions as smart quiver control, smart stability control, smart monitoring, etc in civil engineering. This is a new research field, so at present, many problems are still in their initial stage.
This thesis advances a new method of embedding piezoelectric piles to the common steel structure to form the smart active control element in the structure, that is, the pivot element bar. And this element can check as well as drive, so it can actively control the stability in the steel structure or its member.
Based on the above considerations, first of all, the stability equation of the pivot element bar with piezoelectric piles embedded is deduced in both cases of static forces and dynamic forces, with both cases of non-mechanic-electric couple and mechanic-electric couple taken into considerations. Besides, the effect on the stability of the pivot element bar by the length and supply of the piezoelectric pile is demonstrated with calculations. Then, through the same procedures, the analysis of the stability of the pivot element bar is performed, and Mathieu-Hill Equation-the equation of dynamic stability break under the simple harmonic load is reached.
Secondly, with the model as the example, theoretical analysis and calculation by finite element software are used to reach the proper mass of the model node and to find the proper site of the pivot element bar. Through the analysis of the four methods of embedding piezoelectric piles to the pivot element bar, the most appropriately embedding position is found and the most appropriate length of the pile is also reached, thus supplying the theoretical basis in employing piezoelectric materials properly and economically.
At last, the dynamic time history analysis of the model is proceeded with the finite element analysis software. By analyzing and computing the dynamic time history response of the structure without piezoelectric piles embedded, the maximum displacement of the structure and the time curve of typical nodes are reached under various earthquake summits. And likewise, the dynamic time history response is analyzed and computed with piezoelectric piles embedded. And B-R guideline is used in judging the stability of structure. Then by comparing the results of the two cases, the thesis arrives at a natural conclusion that embedding the pivot element bar can delay the stability of the structure. Thus this thesis supplies the theoretical basis for specific jarring table experiments.
引文
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[2] 陈骥．钢结构稳定理论与设计[M]．北京：科学出版社，2003
[3] 王社良，丰定国．抗震结构设计[M]．武汉：武汉理工大学出版社，2001
[4] 高伟．随机参数智能桁架结构主动控制[D]．西安：西安电子科技大学，2001
[5] B. K. Wada, J. L. Fanson, Adaptive structures. Journal of Intelligent Material Systems and Structures[J]. 1990, 1 (2): 157-174
[6] Newnham, R. E. Rauchau, G. R. Smart electroceramics. J. Am. Ceram[J]. Soc., 1991, 74, 463-480
[7] 于铁强．智能结构机电耦合最优控制[D]．北京工业大学，2004
[8] 吴德伦，张志鹏．结构非线性动力稳定性与矩阵函数法[J]．重庆建筑大学学报，1994，16(1)：9-18
[9] 曲淑英．大型空间框架结构的动力稳定性分析[J]．世界地震工程，1998，14(3)：44-67
[10] 李忠学，沈祖炎．广义位移控制法在动力稳定问题中的应用[J]．同济大学学报，1998，26(6)：609-612
[11] 李忠学，沈祖炎等杆系钢结构非线性动力稳定性识别与判定准则[J]．同济大学学报．2000，28(2)：148-151
[12] 陈务军，董石麟，周岱等．不稳定空间展开折叠桁架结构稳定过程分析[J]．工程力学，2000，17(5)：1-6
[13] 周毅锋．杆系结构动力稳定性实用判别准则[D]．上海：同济大学，2003
[14] 郭海山．单层球面网壳结构动力稳定性及抗震性能研究[D]．哈尔滨：哈尔滨工业大学，2002
[15] 戴国欣，王浩科，刘海鑫等．国产轧制 H 型钢梁整体稳定几何控制条件[J]．钢结构．2004，19 (4)：62-64
[16] 范峰，钱宏亮，谢礼立．最不利地震动在网壳结构抗震设计中的应用[J]．世界地震工程，2003，19(3)：17-21
[17] 丁红丽．钢衬壳弹性和塑性热屈曲和后屈曲问题的理论分析和实验研究[D]．北京：清华大学工程力学系，1996
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