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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。
In this paper, the random response and the analytic method of equivalent damping ratio are systematically studied with arbitrary degree of freedom supported general integral type viscoelastic dampers damped structures. First, the general equations of motion of the structure are established. Then, the equations of motion are transformed into the differential and integral mixed seismic response equations of generalized coordinates of modes. Based on the theory of multi-degrees-of-freedom stochastic mean method, The general analytic solutions of amplitude and phase instantaneous joint probability density function, displacement and velocity instantaneous joint probability density function, displacement and velocity transient response variance are deduced. Finally, Equal criteria are used to analyze the same equivalent criterion. The general analytic formula of equivalent damping ratio for each mode of energy dissipation structure is established. According to the combination of CQC and SRSS, an analytical formula of random seismic response variance of energy dissipation structure is given. The general analytical expressions of the stochastic response and the equivalent damping ratio of the vibration modes of the damper with generalized Maxwell dampers and the generalized differential model are obtained. By comparing with the calculation precision of the modal strain energy method of some typical problems, The effectiveness of the proposed method, so that the energy structure can be directly applied to the design of response spectrum method, thus establishing a support with any linear viscosity and viscosity Usually energy dissipation of the damper structure and random response characteristics equivalent damping solution Complete analytical analysis.