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该文采用等效力控制(EFC)来求解在实时子结构试验中的速度差分方程,采用反馈控制取代数学迭代来求解非线性动力方程。谱半径分析表明,由于准确地模拟了速度响应,结合显式Newmark-?算法的等效力控制方法的稳定界限与系统的阻尼系数无关,在不同阻尼比下稳定界限保持为?=2,具有良好的数值特性。而直接预测速度的中心差分法和采用线性插值模拟速度的平均加速度等效力控制方法,其稳定界限随着系统阻尼比的增大而降低,对于过阻尼结构(阻尼比大于1),原本无条件稳定的平均加速度等效力控制方法变为条件稳定:对于阻尼比为1.05的动力系统,其稳定界限为?=1.45。最后,采用该文方法对安装磁流变(MR)阻尼器的单自由度结构的地震响应进行数值分析,结果表明该文方法能正确跟踪结构速度和位移命令,因而对于速度相关型结构体系,具有良好的适用性和精确性。
In this paper, equivalent force control (EFC) is used to solve the velocity difference equation in the real-time substructure test. The feedback control is used to replace the mathematical iteration to solve the nonlinear dynamic equation. The spectral radius analysis shows that the stability limit of equivalent control method combined with explicit Newmark-? Algorithm has nothing to do with the damping coefficient of the system due to accurately simulating the velocity response, and the stability limit is? = 2 with different damping ratios and has good The numerical characteristics. The central difference method of direct prediction velocity and the average acceleration equivalent force control method using linear interpolation simulation velocity decrease with the increase of system damping ratio. For the overdamping structure (the damping ratio is greater than 1), the original unconditional stability The average acceleration equivalent force control method becomes conditionally stable: For a dynamic system with a damping ratio of 1.05, the stability limit is? = 1.45. Finally, the numerical analysis of the seismic response of a single-degree-of-freedom structure with a MR damper is performed using the proposed method. The results show that the proposed method can track the structure velocity and displacement accurately. Therefore, for the velocity-dependent structural system, Has good applicability and accuracy.