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多重调谐质量阻尼器 (MTMD)主要被用来控制结构的侧向振动与大跨桥梁的抖振。目前 ,还未见有国内外学者讨论大跨桥梁结构扭转振动的MTMD控制问题。鉴此 ,本文将研究利用MTMD控制桥梁结构扭转振动的可能性。假设桥梁结构仅存在扭转振动 ,于是桥梁结构可简化为单自由度结构模型。基于建立的桥梁结构的一般MTMD模型的传递函数 ,导出了设置 5种MTMD模型 (MTMD 1～MTMD 5 )桥梁结构转角位移动力放大系数 (DMF)统一解析式。于是 5种MTMD模型的优化准则可定义为设置 5种MTMD模型桥梁结构最大转角位移动力放大系数的最小值的最小化。数值研究表明 ,相对于其它最优的MTMD模型 ,最优的MTMD 1可以提供更好的有效性和鲁棒性而且制作最简单。因此 ,最优的MTMD 1模型是可用于控制大跨桥梁结构扭转振动的最佳MTMD。
Multi-tuned mass damper (MTMD) is mainly used to control the lateral vibration of structures and the buffeting of long-span bridges. At present, no domestic and foreign scholars have discussed MTMD control problems of torsional vibration of long-span bridge structures. In view of this, this article will study the possibility of using MTMD to control bridge structure torsional vibration. Assuming that there is only torsional vibration in the bridge structure, the bridge structure can be simplified to a one-degree-of-freedom structure model. Based on the transfer function of the general MTMD model of the bridge structure, a unified analytic formula for the angular displacement dynamic amplification factor (DMF) of five bridge MTMD models (MTMD 1 ~ MTMD 5) is set up. The optimization criteria for the five MTMD models can then be defined as minimizing the minimum value of the maximum angular displacement power amplification factor for the five MTMD model bridges. Numerical results show that the optimal MTMD 1 can provide better efficiency and robustness than other optimal MTMD models, and the production is the simplest. Therefore, the optimal MTMD 1 model is the best MTMD that can be used to control torsional vibration of long-span bridges.