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

To investigate the vibration control problem of the 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. The mathematical 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, the control output and dimensionless performance index are defined. The effect of the modal control weighting which determines the control output on the optimal parameters and the performance index is analyzed. The optimal weighting that can equalize 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 the classical design method of the TMDs, the effectiveness of the control with distributed TMDs designed by H2 performance criterion is tested and verified, and higher efficiency of the gradient-based optimization method based on H2 performance criterion is confirmed when the number of the distributed TMDs is increased.