Nonlinear Characteristic And Performance Improvement Of Arc Motion Type Tuned Mass Dampers

Tuned mass damper（TMD）is a traditional passive control device with the advantages of simple configuration and convenient design.It has been widely used in high-rise buildings,slender structures,long-span bridges and other engineering structures.According to the motion trajectory of the tuned mass block,TMDs can be divided into two types:translational motion type and arc motion type（that is,cyclic motion in an arc around a fixed point）.TMDs with arc motion mainly include pendulum TMDs（PTMDs）and lever type TMDs.In the previous optimal design of the arc type TMDs,the motion equations are linearized at small rotation angle for simplicity,resulting in simple practical design formulas for engineering application.Actually,the restriction in small mass ratio of TMDs and high cost of installing vibration suppression devices cause that the stroke of arc type TMDs may exceed the linear region with considerable nonlinear effects when the primary structures are subjected to strong typhoon or seismic loadings,especially for high-rise buildings,transmission and wind turbine towers with high frequencies.In order to meet the small rotation angle assumption and working security,the ways of attaching snubbing system or much higher damping than the optimal values are frequently adopted to constrain the large rotation of PTMDs.However,such ways reduce the damping efficiency of PTMDs on mitigating strong wind-induced or seismic vibrations of high-rise buildings,and restrict the protentional applications in slender structures such as transmission towers and wind turbine towers.Therefore,with the aim of breaking through the linear design theory of the arc type TMDs and developing its vibration control technology at large rotation angles,the damping performance and optimal design of the arc type TMDs（that is pendulum and lever type TMDs）,are systematically studied by utilizing theoretical analyses and numerical simulation.The main contents of this paper are as follows:（1）The influence of nonlinear characteristics of PTMDs on structural damping performance is systematically analyzed.The motion equations of a single degree-of-freedom structure attached with a PTMD is established and solved by the numerically verified Van der pol method.Furthermore,the effects of the external load amplitude,mass ratio and inherent damping of primary structures on the frequency response functions of the primary structure and PTMD are systematically explored.An index,namely maximum critical angle that meets the linear assumption,is proposed.The results show that the nonlinearity of the PTMD seriously reduces its vibration reduction efficiency when the primary structure is subjected to external loads with large amplitude,while large mass ratio of the PTMD or inherent damping of primary structures can significantly mitigate the nonlinearity of the PTMD.Moreover,the optimal design of the PTMD with nonlinearity considered is established,resulting in increasing optimal frequency ratio with external load amplitude while little fluctuation of the optimal damping ratio.At last,the influence of the nonlinearity of the PTMD on the wind-induced vibration control of highrise structures is evaluated by taking a multi-degree-of-freedom chimney structure as an example.（2）The pre-tension/compression isochronous spring is introduced to a PTMD,formed as an IS-PTMD,to achieve dual functions of pendulum length adjustment and nonlinearity mitigation.By the appropriate design of the isochronous spring parameters,the third-order nonlinear resilience generated by the PTMD can be eliminated,resulting in the mitigation of the PTMD’s nonlinearity.Parametric analysis of the IS-PTMD on nonlinearity mitigation is conduced,and the results show that the optimized isochronous spring presents good performance in mitigating the nonlinearity of the PTMD,and its linear working stroke is widened by about 170%,thus,ensuring a good control performance.On this basis,if the isochronous spring is pretensioned/compressed,the pendulum length adjustment is further realized and the optimal design of the isochronous spring is established.Furthermore,the effects of length adjustment coefficient on the FRFs of the primary structure and critical rotation angle of the PTMD are analyzed.The proposed optimal design of the IS-PTMD is then verified by the vibrational analysis of Guangzhou New TV Tower.（3）A new tuned lever inerter-like mass damper（TLIMD）is proposed.The dynamic equation of a simple lever mechanism is derived and compared with the definition of an ideal inerter.The characteristics between the two mechanical devices are compared,and the lever is appropriately named as an inerter-like device.Based on the fixed-point theory,the optimal formula of the TLIMD is obtained,and the control performance of the TLIMD is systematically compared with those of the tuned inerter damper（TID）and tuned mass damped inerter（TMDI）in terms of vibration reduction efficiency,suppression bandwidth and parameter’s sensitivity,which reveals the advantages of the TLIMD in reducing the displacement response of the primary structure,widening the suppression bandwidth and reducing the frequency detuning effects.（4）A complete passive parameter retuning method of the TLIMD is proposed to address the problem of field parameters adjustment of the TLIMD and detuning case.Based on the equivalent linearization method where the inherent damping of the primary structure is equivalent to the contribution to its stiffness,the optimal formula of the TLIMD is deduced to minimize the root mean square responses of the primary structure subjected to random loads.Considering the far field,near field with pulse and near field without pulse seismic loads,the damping performance of the TLIMD is evaluated and compared to those of the TID and TMDI.By means of expediently moving the mass lock location on the lever arm,that is the adjustment of lever ratio,a kind of passive parameter retuning methods is proposed to deal with parameters detuning of the TLIMD.The results show that the damping performance of the TLIMD is significantly improved after retuning.（5）The nonlinear dynamics of TLIMD on response of primary structure is studied.Considering the geometric nonlinearity of the lever motion,the incremental harmonic balance method is utilized to analyze the influence of TLIMD’s nonlinearity on the frequency response function of the primary structure.The influences of the TLIMD’s mass ratio,lever ratio,frequency and damping ratios on system responses are carried out systematically.The results show that the period doubling bifurcation occurs at the large external load amplitude,while the detuning of frequency ratio leads to Hopf and saddle node bifurcations.（6）A lever enhanced tuned mass damper（LE-TMD）is proposed,in which the inerter in the IE-TMDs is replaced by a lever.The optimal parameters of the LE-TMD are obtained by the numerical optimization for H_∞ and H₂ norm criteria when the primary structure is subjected to harmonic and white noise excitations respectively.The advantages of the LE-TMD in terms of amplitude suppression of the primary structure,reduction of amplified/inertial mass and damping coefficient are discussed.