Study Of The Nonlinear Characteristic And The Control Performance Of A Nonlinear Tuned Mass Damper

As a device of vibration attenuation and energy dissipation,tuned mass dampers(TMDs)have been extensively applied to control structural displacement caused by seismic load and wind load.In practical engineering,a tuned mass damper(TMD)inherently exhibits nonlinear behavior in terms of stiffness and damping due to its large displacement or the application of a limiting stopper.Therefore,the study of the influence of nonlinear behavior of the TMD on control performance and how to eliminate the adverse nonlinear behavior is of great importance in the process of design.The paper carried out the following works:(1)A nonlinear TMD system consists of the main structure and the nonlinear TMD,which is coupled with the Duffing stiffness.The analysis of the influence of nonlinear behavior of the TMD on control performance and the control characteristic of nonlinear TMD are carried out in this paper.The theoretical results prove that nonlinear behavior can deteriorate the control performance of the TMD.In addition,the optimal frequency ratio of a nonlinear TMD is corresponding to the maximum response of the nonlinear TMD.(2)A new analysis method of a nonlinear TMD is proposed.The proposed analysis method is based on uncoupled system and only to analyze an independent motion equation,which simplifies the process of analysis.The theoretical results illustrate the validity of the new analysis method.The analytic solutions of jump frequency are obtained according to the new analysis method.The high accuracy of the analytic solutions can be verified by comparing with numerical solutions.(3)A modified design of a TMD is presented in consideration of nonlinear behavior of the TMD in the process of design a TMD.The proposed design method is based on the performance indices of the maximum TMD response,and the optimal frequency ratio is determined by jump frequency.The analytic solutions of the optimal frequency ratio that can be utilized to design the nonlinear TMD are obtained.The theoretical results prove that the proposed design method considering the nonlinear behavior of the TMD will improve the control performance of the nonlinear TMD,and the resonance response of the main structure is decreased markedly.(4)The analysis of dynamic response characteristics of a nonlinear TMD and its control performance is carried out experimentally.The frequency-response curve of the nonlinear TMD and the curve of control performance of the nonlinear TMD is obtained.Experimental results prove that there are jump phenomenon produced in 1.77 Hz and multivalued region range from 1.77 Hz to 1.91 Hz in the frequency-response curve of the nonlinear TMD.In the multivalued region,the initial conditions determine which one represents the actual response of the nonlinear TMD.Additional,the optimal frequency ratio based on linear design method is unreasonable when nonlinear behavior of the TMD is considered in design.A better control performance can be obtained when frequency ratio is less than optimal frequency ratio based on linear design method.