Numerical Algorithms Of Time History Analysis On Wind-induced Vibration Response Of Tall Building With FPS-TMD System

With the rapid development of China’s economy,the continuous development and progress in building material performance and construction technology,tall buildings continue to be constructed in recent years,and these heights of tall buildings are becoming taller and taller.These tall buildings are characterized by light weight,high strength,less flexibility,and they are very sensitive to wind loading.In this thesis,a new type of passive structural control device,the Friction Pendulum System Tuned Mass Damper(FPS-TMD System)was selected as the research object,assuming that it was installed atop of tall buildings under wind loading.The second generation Benchmark building for the structure control study was taken as an example,the efficiency of wind vibration control on tall building with FPS-TMD system was studied.The stability and analysis accuracy of different numerical algorithms on the time history on the wind-induced vibration response of such tall building with passive structural control device are investigated and discussed.The main research contents of this thesis are as follows:(1)The mechanical properties of the friction pendulum tuned mass damper system(FPSTMD system)is studied,and the restoring force model and vibration characteristics of the system are investigated.The dynamic equations of tall buildings with FPS-TMD system under wind loading are established and derived.(2)Taking the second generation Benchmark building as an example,the time history of fluctuating along-wind speed was numerically simulated by the harmonic superposition method,and the time history of along-wind loading was obtained by using quasi-steady assumption.(3)The basic theories and implementation methods of various numerical algorithms for time history analysis on multi-degree-of-freedom dynamic equations,including central difference method,Newmark-β method,two model-reduced Newmark-β methods,state space method,precise integration method,Chang algorithm,CR algorithm and Runge-Kutta method,are investigated extensively.According to the basic principle of stability analysis algorithm,the corresponding recursive formula of dynamic response between successive time steps and its amplification matrix was deduced.Choosing different time step for numerical integral method,the numerical solution to the spectral radius of amplified matrix for various numerical algorithms are obtained.Analyzed results show that the state space algorithm is unconditionally stable for numerical analysis on time history of tall building with FPS-TMD system.(4)Four different friction models of FPS-TMD system are introduced: uni-directional constant friction coulomb model,uni-directional variable friction coulomb model,unidirectional variable friction visco-plastic model and uni-directional displacement-based variable friction model.The MATLAB/Simulink simulation modules for the above different algorithms are constructed.Different friction models of FPS-TMD system are used to analyze The wind-induced vibration response of the Benchmark building with FPS-TMD system under the along-and across-wind loading were studied,and the accuracy of numerical analysis results from different algorithms were compared and analyzed.The research results showed that the wind-induced RMS displacement atop of the tall building with the FPS-TMD system is smaller than that from the uncontrolled case without damping devices,which indicated that the FPSTMD system has a more obvious effect on the wind vibration response control of tall building.The numerical analyzed from different friction models and different numerical algorithms on dynamic equations are slightly different.On the premise of guarantee the stability of algorithm,different numerical algorithms were adopted to simulate the wind-induced displacement atop of the tall building with FPS-TMD system,with the Runge-Kutta method was selected as the basis to be compared with numerical results from other algorithms.Analyzed results showed that the numerical algorithms proposed in this thesis are very effective to evaluate the windinduced response of tall building with the FPS-TMD system with adequate stability and precision.