SMA阻尼器控制单自由度结构在地震激励下的平稳随机振动研究
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摘要
对安装有超弹性形状记忆合金(shape memory alloy,简称SMA)阻尼器的单自由度结构在地震激励下的平稳随机振动进行了理论研究:假定地震地面运动是具有平稳过滤有色噪声模型的随机过程,确定了与《建筑抗震设计规范》(GB 50011-2010)相对应的随机地震动模型参数(平稳持时和谱强度因子);建立了SMA阻尼器控制的单自由度结构在平稳地震动过程下的状态方程,并采用随机等价线性化法推导了其平稳反应公式以及基于首超破坏准则的结构动力可靠性公式;通过算例,证明了随机振动解析式是可行的,并指出SMA阻尼器能消耗地震能量,从而有效抑制结构的振动,增加结构动力可靠性。
Theoretical researches on the stationary random vibration of a single-degree-of freedom structure with the superelastic shape memory alloy(SMA) damper subjected to earthquake excitations are carried out. The earthquake ground motion is assumed to be a stationary filtered color noise process, and the parameters of the random earthquake ground motion model(i.e. the stationary duration and the spectral intensity parameter) are determined according to the Code for seismic design of buildings(GB50011-2010). Random state equations of the SMA-damped structure under the stationary filtered color noise excitation are set up. Then, using an stochastic equivalent linearization method, the stationary random seismic responses of the SMA-damped structure are formulated, and the dynamic reliability of the structure is obtained on the basis of the first threshold crossing failure criterion. Numerical simulations prove that the proposed random vibration formulations are correct, and that the SMA damper can decrease the vibration of the structure effectively, and increase the dynamic reliability of the structure attributed to its capability of dissipating the earthquake energy.
Theoretical researches on the stationary random vibration of a single-degree-of freedom structure with the superelastic shape memory alloy(SMA) damper subjected to earthquake excitations are carried out. The earthquake ground motion is assumed to be a stationary filtered color noise process, and the parameters of the random earthquake ground motion model(i.e. the stationary duration and the spectral intensity parameter) are determined according to the Code for seismic design of buildings(GB50011-2010). Random state equations of the SMA-damped structure under the stationary filtered color noise excitation are set up. Then, using an stochastic equivalent linearization method, the stationary random seismic responses of the SMA-damped structure are formulated, and the dynamic reliability of the structure is obtained on the basis of the first threshold crossing failure criterion. Numerical simulations prove that the proposed random vibration formulations are correct, and that the SMA damper can decrease the vibration of the structure effectively, and increase the dynamic reliability of the structure attributed to its capability of dissipating the earthquake energy.
引文
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[16]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:259.Lin Jiahao,Zhang Yahui.Pseudo-excitation method of random vibration[M].Beijing:Science Press,2004:259.(in Chinese)
[2]Parulekar Y M,Reddy G R,Vaze K K,et al.Seismic response attenuation of structures using shape memory alloy dampers[J].Structural Control and Health Monitoring,2010,19(1):102―119.
[3]Asgarian B,Moradi S.Seismic response of steel braced frames with shape memory alloy braces[J].Journal of Constructional Steel Research,2011,67(1):65―74.
[4]Ma H W,Yam M C H.Modelling of a self-centring damper and its application in structural control[J].Journal of Constructional Steel Research,2011,67(4):656―666.
[5]Dong Junhui,Cai C S,Okeil A M.Overview of potential and existing applications of shape memory alloys in bridges[J].Journal of Bridge Engineering,2011,16(2):305―315.
[6]陈云,吕西林,蒋欢军.新型耗能增强型形状记忆合金阻尼器减震性能研究[J].湖南大学学报(自然科学版),2013,40(2):31―38.Chen Yun,LüXinlin,Jiang Huanjun.Seismic performance study on new enhanced energy dissipation SMA damper[J].Journal of Hunan University(Natural Sciences),2013,40(2):31―38.(in Chinese)
[7]张纪刚,刘艳梅,王贤茂.基于PFD-SMA支撑体系的海洋平台结构振动控制研究[J].工程力学,2013,30(增刊):338―342.Zhang Jigang,Liu Yanmei,Wang Xianmao.Research of vibration control of offshore platform structure based on the PFD-SMA brace system[J].Engineering Mechanics,2013,30(Suppl):338―342.(in Chinese)
[8]Hedayati D F,Alam M S.Performance-based assessment and design of FRP-based high damping rubber bearing incorporated with shape memory alloy wires[J].Engineering Structures,2014,61:166―183.
[9]Jennings E,van de Lindt J W,Ziaei E,et al.Retrofit of a soft-story woodframe building using SMA devices with full-scale hybrid test verification[J].Engineering Structures,2014,80:469―485.
[10]孙广俊,李爱群.安装粘滞阻尼消能支撑结构随机地震反应分析[J].振动与冲击,2009,28(10):117―121,229.Sun Guangjun,Li Aiqun.Random earthquake response analysis for an energy dissipation structure adding viscous dampers[J].Journal of Vibration and Shock,2009,28(10):117―121,229.(in Chinese)
[11]任文杰,李宏男.单自由度SMA阻尼结构在高斯白噪声激励下的平稳随机振动分析[J].工程力学,2014,31(2):35―40.Ren Wenjie,Li Hongnan.Analyses of stationary random vibration of single-degree-of-freedom structure with shape memory alloy damper subjected to Gaussian white noise excitation[J].Engineering Mechanics,2014,31(2):35―40.(in Chinese)
[12]GB50011-2010,建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.GB50011-2010,Code for seismic design of buildings[S].Beijing:China Architecture Industry Press,2010.(in Chinese)
[13]欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,1991,11(3):45―53.Ou Jinping,Niu Ditao,Du Xiuli.Random earthquake ground motion model and its parameter determination used in aseismic design[J].Earthquake Engineering and Engineering Vibration,1991,11(3):45―53.(in Chinese)
[14]袁泉,孙彦杰.随机地震动态模型参数修正[J].科学技术与工程,2011,11(28):7011―7015.Yuan Quan,Sun Yanjie.The modification of random seismic model parameters[J].Science Technology and Engineering,2011,11(28):7011―7015.(in Chinese)
[15]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998:121―150,260―264,290―373.Ou Jinping,Wang Guangyuan.Random vibration of structure[M].Beijing:Higher Education Press,1998:121―150,260―264,290―373.(in Chinese)
[16]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:259.Lin Jiahao,Zhang Yahui.Pseudo-excitation method of random vibration[M].Beijing:Science Press,2004:259.(in Chinese)