粘滞和粘弹性阻尼器减震结构的随机响应特性
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摘要
利用积分型本构关系,针对带支撑任意线性粘滞和粘弹性阻尼器单自由度耗能结构,建立了微分和积分混合地震响应方程;基于随机平均分析法,推导出耗能结构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、振幅动力可靠性、振幅首超时间任意阶统计矩的一般解析解;给出了带支撑广义Maxwell阻尼器和广义微分模型阻尼器耗能结构上述各种随机响应特性,从而建立了带支撑任意线性粘滞和粘弹性阻尼器单自由度减震结构的各种随机响应特性分析的统一解析解法。
By employing integral constitutive relations of dampers,the dynamic integro-differential earthquake response equation of SDOF dissipation structure with supporting brace and viscous and viscoelastic dampers in series is firstly established;By using stochastic averaging method,the analytical solutions of transient joint probability density function for structural amplitude and phase,for structural displacement and velocity are derived,the analytical solutions of transient mean-square values of structural displacement and velocity are established and the analytical solutions of structural amplitude dynamic reliability and arbitrary-order moments of amplitude first-passage time are obtained.The analytical formulas of the foregoing various random response characteristics for SDOF dissipation structure with supporting brace and generalized Maxwell model dampers and generalized differential model dampers in series are given,so the complete analytical solutions of the foregoing various random response characteristics for SDOF dissipation structure with supporting brace and arbitrary linear viscous and viscoelastic dampers in series are achieved.
By employing integral constitutive relations of dampers,the dynamic integro-differential earthquake response equation of SDOF dissipation structure with supporting brace and viscous and viscoelastic dampers in series is firstly established;By using stochastic averaging method,the analytical solutions of transient joint probability density function for structural amplitude and phase,for structural displacement and velocity are derived,the analytical solutions of transient mean-square values of structural displacement and velocity are established and the analytical solutions of structural amplitude dynamic reliability and arbitrary-order moments of amplitude first-passage time are obtained.The analytical formulas of the foregoing various random response characteristics for SDOF dissipation structure with supporting brace and generalized Maxwell model dampers and generalized differential model dampers in series are given,so the complete analytical solutions of the foregoing various random response characteristics for SDOF dissipation structure with supporting brace and arbitrary linear viscous and viscoelastic dampers in series are achieved.
引文
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[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,龙旭.结构被动耗能减振效果的参数影响[J].地震工程与工程振动,1998,18(1):60-70.
[4]李创第,葛新广.带五种被动减振器的高层建筑基与Davenport谱随机风振响应的解析解法[J].工程力学,2009,33(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]欧进萍,吴斌,龙旭.消能减震结构的设计[M].北京:中国建筑工业出版社,2005:323-330.
[9]张义同.热粘弹性理论[M].天津:天津大学出版社,2002.
[10]Park S W.Analytical modeling of viscoelastic dampers for structuraland vibration control[J].International Journal of Solids and Structures,2001,38:8065-8092.
[11]朱位秋.随机振动[M].北京:科学出版社,1998.
[12]Zhu W Q,Cai G Q.Nonlinear stochastic dynamics:a survey of recentdevelopments[J].Acta Mechanica Sinica,2002,18(6):551-566.
[13]Zhu W Q.Nonlinear stochastic dynamics and control in Hamiltonianformulation[J].Applied Mechanics Reviews,2006,59(6):230-248.
[14]张渭滨.数学物理方程[M].北京:清华大学出版社,2007.
[15]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.
[16]Larionov G S.Investigation of vibration of relaxing systems by theaveraging method[J].Mechanics of Polymers,1969,5:714-720.
[17]Lennox W C,Fraser D A.On the first-passage distribution forenvelope of nonstationary narrow-band stochastic process[J].Journalof Applied Mechanics,1974,41(3):793-797.
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