简谐激励下双调谐质量阻尼器基本特性研究

摘要

Based on advantages and disadvantages of tuned mass damper (TMD)and multi-tuned mass damper (MTMD)in civil engineering vibration control,considering the economic efficiency and the applicability of a vibration-reduction device for structures,a double-tuned mass damper (DTMD)was presented.The motion equation of a DTMD with SDOF system under simple-harmonic excitations was established.The dynamic magnification factor (DMF ) expression of the DTMD-SDOF system was derived.An optimization strategy and an evaluation function to judge performances of DTMD were proposed.A parameter optimization program written with MATLAB was used to optimize DTMD.The effect of each parameter on the dynamic magnification factor was analyzed and the robustness of DTMD was evaluated.When the damping ratio of the damper and the natural frequency of the structure controlled were changed. Finally,the effectiveness and the robustness of DTMD were compared with those of TMD and MTMD.The theoretical and numerical results showed that the effectiveness of DTMD is much better than that of TMD and MTMD,and DTMD has the best robustness to the perturbation of the controlled structure frequency;so,DTMD is a very effective device of vibration control.%借鉴 TMD 和 MTMD 各自的优缺点，结合土木工程结构减震装置的经济性和适用性，提出一种双调谐质量阻尼器（DTMD），建立了简谐激励作用下单自由度 DTMD 控制体系（DTMD-SDOF）的运动方程，推导其动力反应放大系数，提出了针对 DTMD 的调优策略及优化评价函数，并通过相关算法获得 DTMD-SDOF 系统的参数优化程序，并利用该程序得到了 DTMD 的最优参数；具体分析了不同参数对 DTMD 共振峰值和调频宽度的影响，并对阻尼器阻尼参数或受控结构频率发生变化后 DTMD 的鲁棒性进行了评价；对 DTMD 与 TMD、MTMD 的有效性和鲁棒性进行了对比分析。理论与数值研究结果表明，DTMD 的控制效果明显优于 TMD 和 MTMD，并且对主结构频率的摄动拥有更佳的鲁棒性。事实证明， DTMD 比 TMD 和 MTMD 更具工程适用性。