Analysis Of Nonlinear Behavior Of A Tuned Mass Damper

Contents of the abstract.Tuned mass damper can effectively control the displacement of the structure under wind load and earthquake,and avoid the structure being destroyed.At present,the research on TMD is mostly exploring new kind of dampers,but the research on TMD design is relatively few.The traditional TMD design method does not consider the non-linear behavior(traditional design method)that TMD may produce in practical application.The research proves that the nonlinear behavior of TMD may have adverse impact on vibration control.Therefore,studying the design method of nonlinear TMD has a great importance.Li Luyu and Cui Peng put forward an improved design method based on the traditional design method,which considered the nonlinearity of TMD in the design process,and the vibration control under the condition of hardening stiffness nonlinearity is effectively improved.However,the improved design method still has some shortcomings,which need to be further studied.According to the above research status,the research contents of this paper are as follows:(1)Constructing a single-degree-of-freedom structural model,while the vibration is controlled by a nonlinear TMD with Duffing stiffness,as the main research object of this paper.For controlling the vibration of multi-degree-of-freedom structures,the critical nonlinearity coefficient is proposed to measure when the nonlinearity of TMD is strong enough that the nonlinearity should be taken into account in the design of TMD.Then using numerical simulation to verify the coefficient with two engineering examples.(2)By means of numerical simulation,the reasons for the errors in the improved design method are analyzed.This method assumes that the TMD has the best control effect when structure has the minimum displacement in the case of structural resonance.While the assumption is unreasonable,especially under the condition of softening stiffness nonlinearity.The improved design method has limitations and is only suitable for TMD with small mass ratio and hardening stiffness nonlinearity,in which condition the negative influence of nonlinearity can be effectively eliminated.(3)The harmonic balance method is used to solve the motion equation.Combining the solution of harmonic balance method with numerical simulation,the nonlinear TMD is designed(HBM design method).After that,using traditional design method,improved design method and HBM design method to design hardening and softening stiffness nonlinear TMDs,and comparing their control effect.It is concluded that the TMD designed by HBM design method has the best control effect in both hardening and softening conditions.(4)Experiments prove that when the hardening stiffness nonlinearity is generated in TMD,the optimal control effect of TMD designed by traditional design method can no longer be obtained,and even deteriorates the control effect of TMD in a certain frequency band.The actual optimal frequency of TMD is less than the optimal frequency designed by traditional design method.When the relative displacement of TMD is maximum,the structure has approximately the minimum displacement.