Maxwell阻尼减震结构的最大非平稳响应
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摘要
研究了设置带支撑Maxwell粘滞阻尼器的多层建筑结构的最大非平稳地震响应,建立了结构一般运动方程,根据多层结构的运动性能,将运动方程按结构第一振型展开,将原结构化成振型广义坐标的单自由度微分与积分混合运动方程;并运用随机平均法,获得了结构随机平均ItO赞方程的解析式,以及位移与速度联合概率密度函数、位移方差和速度方差最大值的一般近似解析解;同时基于与随机平均法分析完全相同的等效原则,获得了结构第一振型的等效阻尼比,使耗能结构可直接应用于反应谱法进行工程设计;最后,针对几种典型的非平稳地震激励模型,获得了最大非平稳方差响应的具体解析解.
The maximum response of multilayer building with supporting brace and Maxwell dampers in series subjected to non-stationary random seismic excitation is studied.Firstly,the structural dynamic equations are established.Then,by using structural model analytical method,the structural first-model dynamic intergro differential equation is got.And then,by using stochastic averaging method,the structural stochastic averaging equations are established,and the analytical solutions of transient joint probability density function for structural displacement and velocity and of maximum mean-square values for structural displacement and velocity are got;And then,by the equivalent criterion of which all random response characteristics are same in the meaning of stochastic averaging analysis,the analytic formulas of structural first-model equivalent damping ratio is achieved,which makes it possible for structure to use response spectrum method technique.Finally,the maximum of nonstationary seismic response of some typical non-stationary earthquake excitation models are given.
The maximum response of multilayer building with supporting brace and Maxwell dampers in series subjected to non-stationary random seismic excitation is studied.Firstly,the structural dynamic equations are established.Then,by using structural model analytical method,the structural first-model dynamic intergro differential equation is got.And then,by using stochastic averaging method,the structural stochastic averaging equations are established,and the analytical solutions of transient joint probability density function for structural displacement and velocity and of maximum mean-square values for structural displacement and velocity are got;And then,by the equivalent criterion of which all random response characteristics are same in the meaning of stochastic averaging analysis,the analytic formulas of structural first-model equivalent damping ratio is achieved,which makes it possible for structure to use response spectrum method technique.Finally,the maximum of nonstationary seismic response of some typical non-stationary earthquake excitation models are given.
引文
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[15]Amin,M,and Ang,A-H S,Nonstationary stochastic model of earthquake motions[J].Journal of Engineering Mechanics Division,1968,94(2):559-584.
[2]周云.粘弹性阻尼减震结构设计[M].武汉:武汉理工大学出版社,2006.
[3]李创第,葛新广.带五种被动减振器的高层建筑基于Daveaport谱随机风振响应的解析解法[J].工程力学,2009,26(4):144-152.
[4]Singh.M.P.etal.Seismic analysis and design with Maxwell dampers[J].Journal of Engineering Mechanics 2003,129(3):273-282.
[5]朱位秋.非线性随机振动理论的近期发展[J].力学发展,1994,24(2):163-172.
[6]Zhu.W.Q.Recent development and application of the stochastic averaging method in random vibration[J].Applied MechanicsReviews,1996,49(10):72-80.
[7]Zhu.W.Q.Nonlinear stochastic dynamics a survey of recent development[J].Acta MechanicaSiuia,2002,18(6):551-566.
[8]朱位秋.随机振动[M].北京:科学出版社,1998.
[9]李创第,邹万杰.非线性流滞阻尼器耗能结构随机地震响应和首超时间分析[J].振动与冲击,2007,26(11):87-90.
[10]李创第,余亚平,陆运军,等.Maxwell粘滞阻尼器耗能结构的高效阻尼分析[J].广西工学院学报,2011,22(1):1-6.
[11]李创第,朱倍权,葛新广.基础隔震结构多振型随机地震响应分析[J].广西工学院学报,2008,19(2):1-4.
[12]Larionov,G.S.Investigation of vibration of relaxing systems by the averaging method[J].Mechanics of Polymers,1969,5:714-720.
[13]Housner,G W,and Jennings,P C.Generation of artificial earthquakes[J].Journal of Engineering and structural Dynamics,1964,90(1):113-150.
[14]Cornell,C A.Stochastic process models in structural engineering[R].Technical report NO.34,Department of Civil Engineering,Standford University,Standford,Calif.,May,1960.
[15]Amin,M,and Ang,A-H S,Nonstationary stochastic model of earthquake motions[J].Journal of Engineering Mechanics Division,1968,94(2):559-584.
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