多自由度Maxwell阻尼器减震结构(Ⅰ)——随机响应特性
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摘要
对多自由度带支撑Maxwell粘滞阻尼器减震结构的随机响应特性进行了系统研究。建立了结构一般运动方程;将运动方程按原结构振型展开,将运动方程化为振型广义坐标的微分和积分混合地震响应方程组;基于多自由度随机平均法理论,获得了结构随机平均It方程组的解析式,推导出耗能结构各振型振子的振幅与相位瞬态联合概率密度函数、位移与速度瞬态联合概率密度函数、位移与速度瞬态响应方差的一般解析解;根据SRSS组合方法,给出了耗能结构随机地震响应方差的一般解析式,从而建立了此类耗能结构随机响应特性分析的完备解析解法。
The random earthquake response characteristics of arbitrary MDOF dissipation structures with supporting brace and Maxwell dampers in series are studied systematically.The structural response equations are firstly established,then,by using modal analytical method,the dynamic integral-differential modal earthquake response equations are established,and then,by using MDOF stochastic averaging method,the structural stochastic averaging It equations are established,the analytical formulas of drift vector and diffusion matrix of averaging It equations are given,the analytical solutions of transient joint probability density function for every structural modal amplitude and phase,for every structural modal displacement and velocity are derived,the analytical solutions of transient mean-square values of every structural modal displacement and velocity are established,lastly,by SRSS methods,the analytic formulas for transient mean-square values of displacement and velocity of the foregoing MDOF dissipation structures are given,so the complete analytical methods for random earthquake response characteristics of arbitrary MDOF dissipation structures with supporting brace and Maxwell dampers in series are established.
The random earthquake response characteristics of arbitrary MDOF dissipation structures with supporting brace and Maxwell dampers in series are studied systematically.The structural response equations are firstly established,then,by using modal analytical method,the dynamic integral-differential modal earthquake response equations are established,and then,by using MDOF stochastic averaging method,the structural stochastic averaging It equations are established,the analytical formulas of drift vector and diffusion matrix of averaging It equations are given,the analytical solutions of transient joint probability density function for every structural modal amplitude and phase,for every structural modal displacement and velocity are derived,the analytical solutions of transient mean-square values of every structural modal displacement and velocity are established,lastly,by SRSS methods,the analytic formulas for transient mean-square values of displacement and velocity of the foregoing MDOF dissipation structures are given,so the complete analytical methods for random earthquake response characteristics of arbitrary MDOF dissipation structures with supporting brace and Maxwell dampers in series are established.
引文
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[16]李创第,葛新广,陆运军.粘滞和粘弹性阻尼器减震结构的随机响应特性[J].应用力学学报,2011,28(3):219-225.
[17]李创第,葛新广,陆运军.粘滞和粘弹性阻尼器减震结构的等效阻尼[J].应用力学学报,2011,28(4):328-333.
[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]欧进萍,吴斌,龙旭.耗能减震结构的抗震设计方法[J].地震工程与工程振动,1998,18(2):98-107.
[4]李创第,葛新广.带五种被动减振器的高层建筑基于Davenport谱随机风振响应的解析解法[J].工程力学,2009,26(4):144-152.
[5]李创第,黄天立.TMD控制优化设计与振动台试验研究[J].土木工程学报,2006,39(7):19-25.
[6]Palmeri A,Ricciardelli F.State space formulation for linearviscoelastic dynamic systems with memory[J].Journal of EngineeringMechanics,2003,129(7):715-724.
[7]Singh M P,Verma N P.Seismic analysis and design with Maxwelldampers[J].Journal of Engineering Mechanics,2003,129(3):273-282.
[8]朱位秋.随机振动[M].北京:科学出版社,1998.
[9]Zhu W Q,Cai G Q.Nonlinear stochastic dynamics:a survey of recentdevelopments[J].Acta Mechanica Sinica,2002,18(6):551-566.
[10]Zhu W Q.Nonlinear stochastic dynamics and control in Hamiltonianformulation[J].Applied Mechanics Reviews,2006,59(6):230-248.
[11]朱位秋.非线性随机动力学与控制-Hamiltonian理论体系框架[M].北京:科学出版社,2003.
[12]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.
[13]李创第,夏立志,葛新广.Maxwell粘滞阻尼器耗能结构的随机地震响应[J].桂林理工大学学报,2011,31(1):61-67.
[14]李创第,刘伟,葛新广.带支撑分数导数粘滞阻尼器减震结构的随机响应[J].广西大学学报,2011,36(1):26-36.
[15]李创第,骆鸿林,陆运军等.分数导数粘滞阻尼器减震结构的随机响应与等效阻尼[J].桂林理工大学学报,2011,31(2):213-220.
[16]李创第,葛新广,陆运军.粘滞和粘弹性阻尼器减震结构的随机响应特性[J].应用力学学报,2011,28(3):219-225.
[17]李创第,葛新广,陆运军.粘滞和粘弹性阻尼器减震结构的等效阻尼[J].应用力学学报,2011,28(4):328-333.
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