分布式TMD对双密频结构的减振研究

针对密集频率结构的减振问题,以典型的2自由度对称结构为例,研究基于H2性能的梯度优化法对密集模态振动减振的分布式TMD(tuned mass dampers)的参数优化和减振效果。建立适合闭环静力反馈控制的组合系统模型,将基于H2性能的梯度优化法扩展至分布式TMD的参数优化;定义针对密集模态振动的控制输出和无量纲评价指标,分析了控制输出的模态控制权重对优化参数和评价指标的影响,指出能使评价指标峰值相等的模态控制最优权重,进一步给出优化参数和评价指标随模态密集度的变化规律;与经典方法对TMD的设计相对比,分析和验证了基于H2性能优化的分布式TMD的良好减振效果,并确认在TMD个数增多时基于H2性能的梯度优化法将具有更佳的优化效果。

Study of vibration control of 2 DOF structure with closely spaced frequencies using distributed TMDs

To investigate vibration control problem of structures with closely spaced frequencies, a typical symmetrical structure with two degree of freedom is taken as a case study. Parameter optimization and control performance of distributed tuned mass dampers(TMDs) for the vibration control of the structure with closely spaced modes are studied by using H2 performance criterion and gradient-based optimization method. Mathematical system model that combines the distributed TMDs and the structure is formulated to represent a closed loop system with a static output feedback control action. The gradient-based optimization method based on H2 performance criterion is extended to the parameter optimization of the distributed TMDs. To control the vibration with closely spaced modes, control output and nondimentional performance index are defined. Effect of modal control weighting forming the control output on the optimal parameters and the performance index is analyzed. The optimal weighting that can equalise two peak values of the performance index is specified. Then change regulations of the optimal parameters and the performance index against density of the closely spaced frequencies are formulated. Compared with classical design method of the TMDs, effective control performance of the distributed TMDs designed by H2 performance criterion is tested and verified. High efficiency of the gradient-based optimization method based on H2 performance criterion is confirmed especially when number of the distributed TMDs is enlarged.