基于复振型分解的多自由度非线性体系动力可靠性研究
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摘要
提出了基于复模态理论的多自由度非线性体系动力可靠性分析方法。该方法首先采用等效线性化的方法处理体系的非线性问题,然后采用复模态分析处理非经典的等效线性阻尼矩阵,将具有非经典阻尼的等效多自由度线性体系按复振型分解,将多自由度体系的随机反应分解为一系列一阶体系的复模态反应,从而求得体系的随机反应,最后进行体系的动力可靠度计算。通过算例验证,表明该方法概念明确、思路清晰,为一般多自由度非线性体系提供了一个普遍适用的动力可靠性分析方法。
Dynamic reliability analysis method for multi-degree of freedom nonlinear system based on complex modal theory is proposed.The method uses equivalent linear method to deal with the nonlinear problems of the system firstly.Then complex modal analysis is used to deal with the non-classical equivalent linear damping matrix,the equivalent MDOF linear system,the damping of which is non-classical,is uncoupled according to the complex mode,that is,the random responses of MDOF system are uncoupled to a series of first-order system of complex modal responses,thus the random responses of the system are obtained,and finally the system dynamic reliability calculation can be done.By example checking,the method is a universal dynamic reliability analysis method for general multi-degree-of-freedom nonlinear system with clear concept and clear thinking.
Dynamic reliability analysis method for multi-degree of freedom nonlinear system based on complex modal theory is proposed.The method uses equivalent linear method to deal with the nonlinear problems of the system firstly.Then complex modal analysis is used to deal with the non-classical equivalent linear damping matrix,the equivalent MDOF linear system,the damping of which is non-classical,is uncoupled according to the complex mode,that is,the random responses of MDOF system are uncoupled to a series of first-order system of complex modal responses,thus the random responses of the system are obtained,and finally the system dynamic reliability calculation can be done.By example checking,the method is a universal dynamic reliability analysis method for general multi-degree-of-freedom nonlinear system with clear concept and clear thinking.
引文
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[2]刘高,林家浩,王秀伟.基于首超破坏机制的大跨斜拉桥抖振动力可靠性分析[J].应用力学学报,2004,21(3):53-57.LIU Gao,LIN Jiahao,WANG Xiuwei.Dynamic reliability of buffeting responses in long-span cabled-stayed bridges by the first excursion mecha-nism[J].Chinese Journal of Applied Mechanics,2004,21(3):53-57.(in Chinese)
[3]杨伟军,林立,杨春侠.混凝土多孔砖砌体房屋抗震可靠度分析[J].工程力学,2007,24(10):100-104.YANG Weijun,LIN Li,YANG Chunxia.The research on the seismic reliability of concrete perforated brick of masonry structure[J].EngineeringMechanics,2007,24(10):100-104.(in Chinese)
[4]柳春光,杜勇刚,刘鑫.基于反应谱法的多点激励下桥梁结构抗震可靠性分析[J].防灾减灾工程学报,2007,27(3):270-274.LIU Chunguang,DU Yonggang,LIU Xin.Seismic reliability analysis of bridge structures subjected to multi-support excitations by response spec-trum method[J].Journal of Disaster Prevention and Mitigation Engineering,2007,27(3):270-274.(in Chinese)
[5]陈文元,赵雷,钟强文,等.基于响应面法的连续刚构地震可靠度分析[J].地震工程与工程振动,2009,29(3):45-50.CHEN Wenyuan,ZHAO Lei,ZHONG Qiangwen,et al.Seismic reliability analysis of rigid frame bridge based on response surface method[J].Journal of Earthquake Engineering and Engineering Vibration,2009,29(3):45-50.(in Chinese)
[6]李杰,陈建兵.随机振动理论与应用新进展[M].上海:同济大学出版社,2009.LI Jie,CHEN Jianbing.New development of random vibration method and application Structures[M].Shanghai:Tongji University Press,2009.(in Chinese)
[7]胡太彬,陈建军,王小兵,等.随机参数多自由度体系在平稳随机反应下的系统动力可靠性[J].应用力学学报,2006,23(4):627-630.HU Taibin,CHEN Jianjun,WANG Xiaobing,et al.System dynamic reliability of multi-degree-of-freedom stochastic structure under stationary ran-dom response[J].Chinese Journal of Applied Mechanics,2006,23(4):627-630.(in Chinese)
[8]周锡元,董娣,苏幼坡.非正交阻尼线性振动系统的复振型地震响应叠加分析方法[J].土木工程学报,2003,36(5):30-36.ZHOU Xiyan,DONG Di,SU Youpo.New method for linear systems with non-classical damping under ground motion[J].China Civil EngineeringJournal,2003,36(5):30-36.(in Chinese)
[9]李创第,朱力华.带TLD结构基于Davenport谱随机风振响应分析和风荷载取值的复模态法[J].应用力学学报,2006,24(1):219-222.LI Chuangdi,ZHU Lihua.Complex methods for random wind-induced response and equivalent wind action of structures with TLD[J].ChineseJournal of Applied Mechanics,2006,24(1):219-222.(in Chinese)
[10]李创第,丁晓华,陈俊忠,等.基础隔震结构基于Clough-Penzien谱随机地震响应分析的复模态法[J].振动与冲击,2006,25(5):162-165.LI Chuangdi,DING Xiaohua,CHEN Junzhong,et al.Complex modal method for analysis of random earthquake response of structures with base i-solation on basis of Clough-Penzien spectrum[J].Journal of Vibration and Shock,2006,24(1):162-165.(in Chinese)
[11]A H-S ANG,TANG W H.Probability concepts in engineering—emphasis on applications to civil and environmental engineering[M].John Wi-ley&Sons Ltd,2007.
[12]张振浩.结构动力可靠性理论研究及RC梁桥抗震可靠性分析[D].长沙:长沙理工大学,2010.ZHANG Zhenhao.Research on structural dynamic reliability theory and seismic reliability analysis of reinforced concrete beam bridge[D].Changsha:Changsha University of Science and Technology,2010.(in Chinese)
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