毗邻建筑地震响应LQG控制问题的闭合解
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摘要
本文把毗邻建筑的地震反应控制作为ＬＱＧ控制问题，并应用虚拟激励法和留数定理推导出问题的闭合解。利用此闭合解研究了加权矩阵Ｑ和Ｒ对建筑阻尼及地震响应的影响。结果表明选用适当的加权矩阵，ＬＱＧ控制可同时有效地减小两栋建筑的地震响应。
Closed form solution of LQG problem for seismic response of adjacent buildings connected by hydraulic actuators is presented in this paper. The closed form solution for seismic response of the system is derived in terms of the pseudo- excitation method and the residue theorem. By using the closed form solution, extensive studies on weighting matrices Q and R can be carried out for the buildings of many degrees of freedom. The results show that if the weighting matrices are se- lected appropriately, the modal damping ratios of the system can be significantly increased and the seismic responses of both buildings can be considerably reduced.
Closed form solution of LQG problem for seismic response of adjacent buildings connected by hydraulic actuators is presented in this paper. The closed form solution for seismic response of the system is derived in terms of the pseudo- excitation method and the residue theorem. By using the closed form solution, extensive studies on weighting matrices Q and R can be carried out for the buildings of many degrees of freedom. The results show that if the weighting matrices are se- lected appropriately, the modal damping ratios of the system can be significantly increased and the seismic responses of both buildings can be considerably reduced.
引文
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[2] Kasai K. Maison B F. Building pounding damage during the 1989 Loma Prieta earthquake[J]. Engineering Structures, 1997,19(3): 195 - 207.
[3] Westermo B. The dynatmics of interstructural connection to prevent pounding[J], Earthquake Engng. Struct. Dyn.. 1989, 18(5): 687 - 699.
[4] Kobori T, Yamada T, Takenaka Y. Maeda Y. Nishimura I. Effect of dynamic tuned connector on reduction of seismicresponse-application to adjacent office buildings[A]. In: Proc. of the Ninth World Conf. on Earthquake Engineering[C].Tokyo-Kyoto. Japan, V. 1988: 773 - 778.
[5] Zhang W S, Xu Y L. Dynamic characteristies and seismic response of adjacent buildings linked by discrete dampers[A],Earthquake Engng. Struct. Dyn[C], 1999. 28(10): 1163 - 1185.
[6] Qi X X. Chang K L. Study of application of viscous dampers in seismic joints[A]. Proceedings of the International Confer-ence on Structural Dynamics, Vibration. Noise and Control[C]. HongKong, 1995: 286-291.
[7] Soong T T. Active structural control : theory and practice[M]. London: Longman and New York: Wiley,1990.
[8] Housner G W. Bergman L A. Caughey T K, Chassiakos A G. Claus R O, Masri S F, Skelton R E, Soong T T. Spencer BF, Yao J T P. Structural control: past, present, and future[J]. J. Engrg. Mech., ASCE, 1997, 123(9):897 -971.
[9] Lin J H., Zhang W S. Li J J. Structural response to arbitrarily coherent stationary random excitations[J]. Computers &Structures, 1994, 50(5): 629 - 633.
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