Vibration Reduction Performance Of Variable Friction Pendulum Tuned Mass Damper

The structural control tuned device and its theoretical model,as well as the vibration（seismic）design method,are fundamental and long-term research focuses in the field of engineering structural vibration（seismic）reduction.In light of the new trend in disaster prevention and mitigation for structures,this paper focuses on iconic high-rise structures and conducts research on new theories for wind-induced vibrations and seismic response control,development of novel devices,and optimal parameter design methods.The underlying mechanisms and influencing laws are also analyzed.This paper employs a combination of theoretical analysis,numerical simulation,and experimental verification to study variable friction pendulum tuned mass damper.The main research work and achievements are as follows:1)A variable friction pendulum tuned mass damper（VFP-TMD）with hysteresis damping（HD）characteristics is proposed.By utilizing the effective friction coefficient provided by the sliding block based on the weighted ratio of contact area,linear variable friction force is achieved and validated through base shear tests.The nonlinear equations of motion for VFP-TMD,characterized by its core HD-TMD,are derived.Based on fixed point theory,precise solutions for design parameters of different performance indicators under seismic excitation are presented for the undamped structure-HD-TMD system.In order to better understand VFP-TMD with HD characteristics,constant friction and multi stage variable friction patterns are compared.Compared to constant friction and multi stage variable friction patterns,VFP-TMD with HD characteristics achieves significant optimization through closed-form solutions.The effectiveness of closed-form solutions in controlling VFP-TMD is verified as well as the superiority of linear variable friction mode in vibration reduction.Results indicate that linear variable friction on VFP-TMD with HD characteristics can be understood as an infinite number of stages of variable frictions,providing"infinite bandwidth"to achieve stable vibration control effects according to excitation amplitude while fully exploring the potential benefits from varying frictions.This lays a solid foundation for further theoretical development and application expansion of pendulum-type tuned mass dampers with HD characteristics.2)Due to the inherent randomness of earthquakes and wind-induced vibrations,the application of residue theorem for obtaining analytical solutions based on H₂ optimization represents a breakthrough in overcoming numerical challenges associated with infinite integrals.This achievement establishes a solid theoretical foundation for efficiently determining various optimal design parameters for HD-TMD in the presence of random white noise conditions.Considering the practical stroke limitations of VFP-TMD,a performance-balanced design for HD-TMD with weighting factors is established based on tolerance conditions,effectively ensuring both vibration reduction performance and robustness.The optimal parameter tables for undamped and damped structures of HD-TMD are obtained through numerical calculations,and the equivalent additional viscous damping of HD-TMD is studied.Engineering examples involving wind loads and earthquake loads demonstrate that adopting performance-balanced design can significantly reduce the stroke range of HD-TMD while ensuring linearity and control robustness in system behavior,exhibiting slightly superior vibration reduction advantages compared to classical viscous damping TMDs.Considering the inevitable presence of other types of damping in practical applications of HD-TMD,a dual damping tuned mass damper（DD-TMD）model that combines viscous damping（VD）and hysteretic damping is studied.It is found that within a certain range of parameter changes,DD-TMD exhibits stable control effects.A DD-TMD parameter optimization method based on stable regions is proposed.The equivalent additional viscous damping ratio provided by DD-TMD for structures is also studied,and optimal parameters are obtained under different main structure damping ratios.This proves that the optimal HD ratio and VD ratio can be transformed relatively to maintain an unchanged equivalent additional viscous damping ratio.3)With the increase in excitation amplitude,the inherent nonlinearity of VFP-TMD pendulum motion becomes more pronounced,leading to uncertainty in vibration and loss of prediction accuracy and control due to linear assumptions.In order to address this issue,HD is introduced into PTMD and nonlinear performance-oriented seismic optimization design is achieved.Two commonly used nonlinear analysis methods（i.e.,slow variation method（K-B method）and stochastic linearization method（SLM method））are employed to illustrate the energy dissipation characteristics of different types of damping.The combination of PTMD with HD reveals detailed attenuation characteristics and exact nonlinear damping properties when combined with PTMD damping.The relation between different damping is confirmed by the exact expression of SLM.To consider the influence of amplitude uncertainty on the structure-PTMD control system,a nonlinear performance optimization design approach based on amplitude robustness index is proposed.Seismic example results validate the applicability of the proposed optimization approach for PTMD with HD;as earthquake excitation increases,PTMD’s damping dissipation capacity increases thereby better protecting structures.4)In a bidirectional motion,the shape of the hysteresis loops in friction pendulum systems undergoes changes and exhibits unexpected dynamic behavior compared to unidirectional motion.A novel bidirectional rail variable friction pendulum tuned mass damper（BRVFP-TMD）is proposed to effectively organize the optimal control frequency in both directions,generate bidirectional full friction force,and achieve bidirectional optimal control,breaking free from the constraints of existing friction pendulum tuned mass dampers in practical bidirectional vibration control processes.Traditional friction pendulum TMD with spherical sliding surfaces is studied as an example using unidirectional harmonic excitation with an attack angle to evaluate its control effectiveness and demonstrate the superiority of BRVFP-TMD over traditional ones in terms of hysteresis loop collapse and mechanism.The influence of TMD placement on high-rise structures is considered,and through fixed-point theory,improved optimal parameter closed-form solutions for BRVFP-TMD considering deployment location and inherent structural damping are obtained.HD is transformed from SLM to equivalent VD,and the analytic solution expression of HD and VD forms is established.Taking the typical high-rise structure of Conton Tower as an example,the peak value of bidirectional displacement frequency response decreases by 35.74%and 47.83%respectively,which shows the superiority of considering the improved optimal solution of deployment position and BRVFP-TMD bidirectional wind-induced vibration control in high-rise engineering cases.5)Consider the influence of structural bending deformation on the VFP-TMD control system,a seismic response model for the shear-bending structure-VFP-TMD system is proposed.The optimization design of VFP-TMD parameters is conducted based on stochastic optimization theory.It is found that there exists a dual rotation angle lever effect between the structural bending rotation angle and the VFP-TMD pendulum rotation angle,leading to control loss in the structure.The equivalent additional damping ratio provided by VFP-TMD to high-rise structures under different shear-bending structure damping ratios is presented.Furthermore,engineering examples are used to verify the effectiveness of optimal parameters for the shear-bending structure-VFP-TMD system.The results show that optimal parameters of VFP-TMD for the shear-bending structure can simultaneously reduce structural displacement and flexural rotation angle,thereby weakening the lever effect.