Analysis Of The Contact Nonlinear Characteristic Of The Tuned Mass Damper

During the normal use stage,buildings will often be attacked by wind and earthquake from time to time.They usually cause unexpected vibration to buildings,which will influence the safety of buildings and the comfort for people.In order to control the vibration,Tuned Mass Damper（TMD）has been widely applied to control unexpected vibration of the building structures.It can effectively reduce the deformation and displacement of structures.When the TMD works,it usually has a displacement relative to the structure.For the earthquake or wind is random,the displacement of TMD is often difficult to predict.If the structure collides with TMD,the safety of the structure will be affected.So it is very important to limit the displacement of TMD.When the limiting stopper is added to the TMD,TMD will have contact nonlinear behavior.It is very important to research the influence of contact nonlinear on the control performance of TMD,and it has great significance to the engineering application of TMD.Based on the contact nonlinearity of TMD,the following studies are carried out in this paper:（1）Constructing a single-degree-of-freedom structural model as the controlled object,a two DOFs system combined with TMD and a SDOF structure is constructed to study the vibration control performance of the TMD.Compared with the original TMD,a limiting stopper with stiffness and damping is added to control the displacement of TMD.The limiting stopper leads to the contact nonlinearity of TMD.The influence of contact nonlinearity of TMD on the control performance of TMD is analyzed.Through numerical simulation method,the limiting device can control the displacement of TMD relative to the structure well,and damping plays a major role in controlling the displacement of TMD.（2）When the limiting stopper is added to the TMD,the system produces a strong nonlinearity.The parameters which need to be searched increase.For the system with limiting stopper,it is difficult to get the analytic solution of the governing equation of motion.Compared with the original system,the TMD without damper and a limiting stopper without stiffness is considered,the original system is simplified.But it is still a piecewise linear system.The simplified system is analyzed by numerical simulation method.（3）For the contact nonlinear TMD with piecewise linearity,it is difficult to analyze it by analytical method.The statistical linearization theory is applied for the analyzing of contact non-linear TMD.The statistical linearization method is carried out to get a equivalent system for the contact nonlinear TMD.The equivalent linear model parameters of the contact nonlinear model are obtained by statistical linearization method,and the time-history curves are compared to verify its effectiveness.For the low accuracy for the system,the equivalent viscous damping theory is applied to get the equivalent linear parameters,which can effectively improve the accuracy.（4）A TMD model with limiting stopper is designed.The control performance of contact nonlinear TMD is analyzed by experiment.The displacement frequency response curves of contact nonlinear TMD and the displacement frequency response curves of structure are measured.The damper used in the experiment has a relatively large damping and a relatively large displacement restriction on TMD.When the damper of the limiting device is large,the control performance of TMD decreases.This is consistent with the view proposed by Cui Peng of the research group before that when TMD displacement is maximum,the control performance is the best in his paper.Further research is needed on how to select the appropriate damper.