Vibration Analysis Of Structure With Tuned Mass Damper Using Real Mode And Complex Mode Decomposition

Many research shows that tuned mass damper(TMD)is an effective structural control technique which can significantly reduce the structural vibration due to wind loads.Most of these studies focused on how to design the optimal TMD system and evaluate the performance of the TMD to reduce the structural vibration.One common method that the sresearcher used to evaluate structural dynamic responses when TMD to treat the effects of the TMD on reducing structural vibration as is installed is adding additional damping ratio to the structure.In this way,the tradition real mode decomposition method can be easily applied to calculate the responses of the structure with TMD system installed.However,the real mode decomposition method may not be able to accurately capture the true responses of the structure,which may lead to underestimating structural internal force,making the structural designed using the real mode decomposition method unsafe.In this study,a vibration analysis method for the structure installed with TMD system is investigated,based on complex mode decomposition.The main structure and TMD system are created as one dynamic system.The dynamic responses of the system are calculated using the real mode decomposition and the complex mode decomposition methods respectively.Further research found that after installing the TMD into the structure,the whole dynamic system(structure + TMD)does not satisfy the orthogonal condition of the damping matrix in the real mode composition.As a result,the real mode decomposition cannot very accurately provide some of the structural responses.On the contrary,not assuming the orthogonality of the damping matrix,the complex mode decomposition method is able to accurately compute structural responses.Moreover,to compare the structural responses from a random vibration point of view using the real mode decomposition and the complex mode decomposition methods respectively,the variance of the structural responses subjected to wind load are derived and verified.Through comparing the variances of the structural responses calculated by the derived formula,it is found that the real mode decomposition will underestimate the variances of some structural responses,making the structural designed base on this method unsafe;on the other hand,the complex mode decomposition method is able to accurately provide the variances of the structural responses.As a conclusion,for the structure installed with TMD system,in order to more accurately calculate the structural responses subjected to wind loads,the complex mode decomposition method is much preferred than the real mode decomposition method.