摘要
该文对任意多自由度带支撑一般积分型粘滞和粘弹性阻尼器减震结构的随机响应与等效阻尼比的解析分析法进行了系统研究。首先建立了结构一般运动方程;然后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;继而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;最后,基于与多自由度随机平均法分析完全相同的等效准则,建立了耗能结构各振型等效阻尼比的一般解析式,并根据CQC和SRSS组合方法,建立了耗能结构随机地震响应方差的解析式,给出了带支撑广义Maxwell阻尼器和广义微分模型阻尼器减震结构随机响应和各振型等效阻尼比的一般解析式,通过与一些典型问题的模态应变能法的计算精度对比分析,表明了所提方法的有效性,使耗能结构可直接应用反应谱法进行设计,从而建立了带支撑任意线性粘滞和粘弹性阻尼器一般耗能结构随机响应与特性等效阻尼分析的完备解析解法。
The complete analytical methods for random earthquake response and equivalent damping of arbitrary MDOF dissipation structures with supporting braces and general integral model viscoelastic dampers in series are studied systematically.The structural response equations are firstly established.Then,by using the modal analytical method,the dynamic integral-differential model earthquake response equations are established.And then,by using the MDOF stochastic averaging method,the structural stochastic averaging It equations are established,the analytical formulas of the drift vector and the diffusion matrix of averaging It equations are given,the analytical solutions of the 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 various structural modal displacements and velocities are established.By the equivalent criterion of which all random response characteristics are identical in the meaning of MDOF stochastic averaging analysis,the analytic formulas of every modal equivalent damping ratio are established,which make it possible for structures to use response spectrum technique.Lastly,by CQC and SRSS methods,the analytic formulas for the random earthquake response of foregoing MDOF dissipation structures are given,the analytical formulas of the foregoing random response characteristics and every structural modal equivalent damping ratio for MDOF dissipation structures with supporting braces and general Maxwell model dampers and general differential model dampers in series are given,it is verified that the proposed methods are effective through accuracy in comparison with the Modal Strain Energy method for some typical problems,so the complete solutions of random earthquake response characteristics and equivalent damping for arbitrary MDOF dissipation structures with supporting braces and arbitrary linear viscous and viscoelastic dampers in series are achieved.
出处
《工程力学》
EI
CSCD
北大核心
2013年第4期136-145,共10页
Engineering Mechanics
基金
广西高校百名中青年学科带头人计划项目(RC20060814017)
广西自然科学基金项目(0481001)
广西科学基金项目(0575021)
广西教育厅科研项目(0508052)
关键词
一般积分型粘弹性阻尼器
支撑
多自由度减震结构
随机平均法
随机响应特性
振型等效阻尼比
反应谱法
general integral model viscoelastic dampers
brace
MDOF dissipation structures
stochastic averaging method
random response characteristics
modal equivalent damping ratio
response spectrum method
