1. State Key Lab for Seismic Reduction Control & Structural Safety (Cultivation), Guangzhou University, Guangzhou 510405, China;
2. College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100122, China
A vibration isolation structure is composed of a superstructure and a vibration isolation layer including vibration isolation bearings and dampers with different damping features from those of superstructure, these dampers possess typically non-proportional damping features. So, the damping matrix of this system can’t be decomposed via the system’s undamped modal shapes and the traditional modal shapes superposition response spectrum method is not applicable to this system. Here, based on the random vibration theory and considering features of vibration isolation structures, a multi-dimensional earthquake complex modal shapes superposition response spectrum method was proposed, it could consider non-proportional damping features. The error of the forced decoupling method, an approximate approach commonly used, was studied. It was found that the energy transfer between the superstructure and the vibration isolation layer is prevented with this method to cause smaller seismic responses of the superstructure. The vibration isolation benchmark model was taken as an example to implement the time-history method, the forced decoupling method and the proposed complex modal shapes superposition response spectrum method, respectively. Three results were compared, it was shown that the proposed method has a better accuracy and can fully reflect the non-proportional damping characteristics in vibration isolation systems; when the damping of the vibration isolation layer is larger, the forced decoupling approach has a worse accuracy, it can’t reflect the amplification effects of the superstructure seismic responses due to damping of the vibration isolation layer.
[1]Cronin D L. Approximation for Determining Harmonically Excited Response of Non-classically Damped System [J]. Journal of Engineering for Industry, 1976, 98:43-47.
[2] Warburton G B, Soni S R. Errors in response calcula-tions for non-classically damped structures [J]. Earth-quake Engineering and Structural Dynamics, 1977, 5(4):365-377.
[3] Traill-Nash R W. An analysis of the response of a damped dynamical system subjected to impress forces [R]. Aust. Dept. Supply, Aero. Res. Lab., Rpt. SM.151, 1950.
[4] Foss F K. Co-ordinates which uncouple the linear dynamic systems [J]. Journal of Applied Mechan-ics-Transactions of the ASME, 1958, 24:361-364.
[5] Igusa T, Kiureghian A D. Response spectrum method for systems with non-classical damping [C] // Proc. ASCE-EMD specialty conf. West Lafayette, Indiana, 1983: 380-384.
[6] Gupta A K, Jaw J W. Response spectrum method for non-classically damped systems [J]. Nuclear Engineering and Design, 1986, 91:161-169.
[7] Villaverde R. Rosenblueth’s modal combination rule for systems with non-classical damping [J]. Earthquake Engineering and Structural Dynamics, 1988, 16:315-328.
[8] Zhou X, Yu R, Dong D. Complex mode superposition algorithm for seismic responses of non-classically damped linear MDOF system [J]. Journal of Earthquake Engineering, 2004, 8(4):597-641.
[9] Song J., Chu Y., Liang Z., Lee G C. Modal analysis of generally damped linear structures subjected to seismic excitations[R]. Technical Report MCEER-08-0005, 2008.
[10] Tsai H, Kelly J. Non-classical damping in dynamic analysis of base-isolated structures with internal equip-ment [J]. Earthquake Engineering and Structural Dynamics, 1988, 16:29-43.
[11]苏经宇,曾德民,田杰.隔震建筑概论[M].北京:冶金工业出版社,2012:32
[12]吕西林,冯德民,施卫星,等.组合基础隔震房屋模型振动台试验研究[J].土木工程学报,2001,34(2):43-49.
LV Xinlin, FENG Demin, SHI Weixing, et al. Shaking table test on building models with comined isolation sys-tem [J]. China Civil Engineering Journal, 2001, 34(2):43-49.
[13]袁涌,朱昆,熊世树,等.高阻尼橡胶隔震支座的力学性能及隔震效果研究[J].工程抗震与加固改造,2008,30(3):15-20.
YAUN Yong, ZHU Kun, XIONG Shishu, et al. Experi-mental Study on Characteristics and Isolator Effect of High-damping Rubber Bearing [J]. Earthquake Resistant Engineering and Retrofitting, 2008, 30(3):15-20.
[14] KELLY J M. The role of damping in seismic isolation [J]. Earthquake Engineering and Structural Dynamics, 1999, 28:3-20.
[15] Narasimhan S, Nagarajaiah S, Johnson EA, Gavin HP. Smart base-isolated benchmark building. Part I: problem definition [J]. Structural Control and Health Monitoring, 2006, 13:573-588.
[16] Penzien, J, Watabe, M. Characteristics of 3-Dimensional earthquake ground motions [J]. Earth-quake Engineering and Structural Dynamics, 1975, 3:365-373.
[17] Clough R W, Penzien J. Dynamics of Structures [M]. McGraw-Hill: New York, 1991:472.