耗能减震结构阻尼器随机地震响应的扩阶复模态分析
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摘要
对两层带Maxwell阻尼器的耗能减震结构在随机地震响应下进行了系统研究,首先建立了结构运动方程,然后用前两个振型将上部结构展开,因所得结构运动方程的刚度、阻尼均为非对称的,因此采用扩阶复模态方法解耦,获得了结构各层在白噪声激励下的随机地震响应解析解。通过算例分析,对两层框架结构设置阻尼器与未设置阻尼器进行对比,得出了设置阻尼器结构的位移响应方差大大小于未设置阻尼器结构的结论,从而实现了阻尼器耗能减震的目的,并建立了两自由度体系在任意非经典阻尼、非对称刚度下随机地震响应解析解分析的一般方法。
In this paper,the random earthquake response of structure with energy dissipation is studied systemtically. The dynamic equations are firstly established,then,the upper structure is expanded with the two modes.According to the situation that the damping is the nonclassical damping and the structure is nonsymmetry,the expansion complex modal method is used to decoupling the equations. In white noise excitation,every layers random earthquake response solution is obtained. Through the example,the two story frame structure with damper and without damper is compared,it is concluded that the displacement response variance of structure with damper is significantly less than the structure without damper,the purpose of the damper energy dissipation is achieved. And the general method of two degree of freedom system in nonclassical damping and asymmetric stiffness on random seismic response is established.
In this paper,the random earthquake response of structure with energy dissipation is studied systemtically. The dynamic equations are firstly established,then,the upper structure is expanded with the two modes.According to the situation that the damping is the nonclassical damping and the structure is nonsymmetry,the expansion complex modal method is used to decoupling the equations. In white noise excitation,every layers random earthquake response solution is obtained. Through the example,the two story frame structure with damper and without damper is compared,it is concluded that the displacement response variance of structure with damper is significantly less than the structure without damper,the purpose of the damper energy dissipation is achieved. And the general method of two degree of freedom system in nonclassical damping and asymmetric stiffness on random seismic response is established.
引文
[1]Housner G W,Bergman L A,Caughey T K,Chassiakos AG,Claus R O,Skelton RE,Soong T T,Spencer B F,Yao J T P.Structure Control:Past,Present,and Future[J].Journal of Engineering Mechanics,1997,123(9):897-905
[2]李宏男,李忠献,祁皑,贾影.结构振动与控制[M].北京:中国建筑工业出版社,2005
[3]周福霖.工程结构减震控制[M].北京:地震出版社,1997
[4]GB 50011—2010,建筑抗震设计规范[S]
[5]欧进萍,刘晶波,杜修力.结构动力学[M].北京:机械工业出版社,2005
[6]Fang.T.Wang.Z.Z.,Stationary Response to Second-order Filtered white Noise Excitation[J].AIAA.J.1986,24(6):1048-1051
[7]李创第,黄天立,李暾,等.带TMD结构随机地震响应分析的复模态法[J].振动与冲击,2003,22(1):36-39
[8]李创第.线性与非线性随机过程时变可靠度理论及其在高层建筑玻璃幕墙非线性抗风抗震设计中的应用[D].武汉:武汉工业大学,1999
[2]李宏男,李忠献,祁皑,贾影.结构振动与控制[M].北京:中国建筑工业出版社,2005
[3]周福霖.工程结构减震控制[M].北京:地震出版社,1997
[4]GB 50011—2010,建筑抗震设计规范[S]
[5]欧进萍,刘晶波,杜修力.结构动力学[M].北京:机械工业出版社,2005
[6]Fang.T.Wang.Z.Z.,Stationary Response to Second-order Filtered white Noise Excitation[J].AIAA.J.1986,24(6):1048-1051
[7]李创第,黄天立,李暾,等.带TMD结构随机地震响应分析的复模态法[J].振动与冲击,2003,22(1):36-39
[8]李创第.线性与非线性随机过程时变可靠度理论及其在高层建筑玻璃幕墙非线性抗风抗震设计中的应用[D].武汉:武汉工业大学,1999
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