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为了研究控制平-扭耦联效应黏弹性阻尼器最优位置问题,推导不同偏心形式单层偏心结构,采用不同方式布置黏弹性阻尼器减震结构考虑平-扭耦联效应的振动方程,建立基于结构平动与扭转位移响应相关性的目标函数。利用随机振动理论中的李雅普诺夫方程和最优控制理论,建立并求解偏心结构平面几何中心位移响应协方差矩阵,通过求得目标函数最小值找到阻尼器的最优偏心位置。在此基础上编制相应程序对典型算例进行数值计算,分析不同偏心形式下,地震荷载输入条件、等效阻尼比、静力偏心率、扭平频率比、结构周期、结构尺寸效应对考虑平-扭耦联效应时黏弹性阻尼器最优位置的影响规律。
In order to study the optimal position control of viscoelastic dampers with flat-torsional coupling effect, eccentric structures with different eccentric forms were deduced, and the vibration equations of viscoelastic dampers were arranged in different ways to consider the vibration response of the flat-torsional coupling effect. The objective function based on the correlation between translational motion and torsional displacement response. The Lyapunov equation and optimal control theory in random vibration theory are used to establish and solve the geometric center displacement response covariance matrix of the eccentric structure. The optimal eccentric position of the damper is found by finding the minimum value of the objective function. On the basis of this, a corresponding program is developed to calculate the typical examples. The effects of different eccentric forms, such as input conditions of seismic load, equivalent damping ratio, static eccentricity, torsional frequency ratio, structure period and structure size, Influence of Optimal Positions of Viscoelastic Dampers on Twisted Coupling Effect.