Control Performance Analysis Of Tuned Mass Damper Based On Higher-order Nonlinear Stiffness

As a kind of energy dissipation device,the tuned mass damper(TMD)can reduce the deformation or displacement of the structure under the action of seismic and wind loads,and has been widely used in the field of structural vibration control.In actual engineering,due to the adverse effects that the nonlinear behavior of TMD may have on structural vibration control,a nonlinear design of TMD is required.At present,the research on nonlinear TMD is mostly based on the ideal cubic stiffness conditions,while the design of TMD with high-order nonlinear stiffness is relatively few.Therefore,it is of great significance to consider the control effect of TMD under the condition of high-order nonlinear stiffness and to reduce or eliminate the adverse effects of nonlinear factors in the process of TMD design.Combined with the above situation,this paper conducts research from the following four aspects:(1)Under the condition of damped forced vibration,a two-degree-of-freedom system composed of a single-degree-of-freedom main structure and a nonlinear TMD system with fivedegree nonlinear stiffness is taken as the analytical model,and the influence of the nonlinear factors of TMD on the vibration control effect is studied by analyzing the control characteristics of the nonlinear TMD.The analysis results show that the nonlinear behavior of TMD will cause the deterioration of its control effect.In addition,The displacement response of the approximate structure is the smallest when the displacement response of the TMD is the largest,and then the nonlinear TMD has a better control effect.(2)When the nonlinearity of the system is weak,the steady-state response of the structure is approximated to the first-order harmonic response,so as to decouple the nonlinear TMD analysis from the whole system.The nonlinear TMD analysis is simplified by analyzing the new independent equations of motion.The analysis results show that the simplified analysis method has the same results as the overall analysis method.By solving the TMD amplitudefrequency relation,the approximate analytical solution of jump frequency is obtained.Comparing the numerical solutions,it can be found that the approximate analytical solution of the hop frequency has sufficient accuracy.(3)Considering the adverse effect of the nonlinear behavior of TMD on its control effect,based on the traditional design method and the jump frequency of the nonlinear TMD,an analytical formula for calculating the optimal frequency ratio of TMD is given.This analytical formula is used to optimize the design of nonlinear TMD.The analysis results show that,compared with the traditional design method,the improved nonlinear TMD design method based on jump frequency can improve the control performance of TMD.(4)In the case that the control effect of the improved design method is not ideal under the softening nonlinear effect,a soft stiffening compensation method with nonlinear stiffness is proposed.Based on the steady-state displacement amplitude of the linear TMD under the same conditions,the method can reduce the displacement response of the main structure by adjusting the hardening stiffness coefficient of the nonlinear TMD.The simulation results show that the new soft hardening compensation method can improve the control performance of TMD under softening nonlinear effects.