Study On The Random Response And Reliability Of Structures Under Non-stationary Earthquakes Based On Bouc-Wen Model

Seismic activity has significant randomness characteristics,therefore,studying the seismic response and dynamic reliability of structures based on random vibration theory is a more reasonable way.Although the stationary random seismic model can simulate the randomness nature of seismic activity,it fails to consider the intensity shown by actual seismic activity and non-stationarity of frequency content.Adopting non-stationary seismic model is closer to the real seismic ground motion,which is in line with the actual situation.When it comes to the non-stationary of the level of frequency,because of the lack of the reasonable quantitative description,as well as the difficulty and complexity of mathematical analysis,the study on seismic ground motion always concentrates on the non-stationary of intensity.On the other hand,under the repeated action of ground vibration,it is difficult for the structure to avoid entering the stage of elastic-plastic work and showing hysteresis nonlinear.So this paper studies the dynamic reliability of the hysteresis nonlinear structure under the action of non-stationary ground vibration based on the random vibration theory,the contents mainly include:(1)Use commonly used white noise,color noise model and corresponding non-stationary excitation model,and solve the response of hysteresis nonlinear systems under different random excitation models by utilizing the cumulant-neglect closure,as the same time,verify the correctness of the calculation results by using Monte Carlo Numerical Simulation Method.On this basis,study the influence of system parameters on system response.The results show that the system damping,the ratio of linear stiffness to non-linear stiffness and the parameters of Bouc-Wen hysteretic model have significant effects on the random response of the hysteretic non-linear random vibrationsubsystem.The second-order mean square response of the system decreases with the increase of damping and increases with the increase of the ratio of linear stiffness to non-linear stiffness.(2)Take single-storey reinforced concrete frame structure as research object,and simulate the hysteresis characteristics of the structure with the classical Bouc-Wen model,at the same time considering the non-stationary characteristics of the seismic action,adopt three non-stationary modal functions to simulate seismic ground motion,solve random seismic response of structures by using the cumulant-neglect closure to get the second order moment function of structural response,and analyze the dynamic reliability of the structure with the theory of exceeding reliability for the first time.At the same time,further study the influence of site conditions,structural stiffness,excitation strength,modal functions and other parameters on the dynamic reliability of frame structures.The results show that under the excitation of non-stationary filtered white noise,the site soil characteristics,structural stiffness and excitation intensity have significant effects on the random seismic response and dynamic reliability of the structure,and the non-stationary modal function has significant effects on the dynamic reliability of the structure.When the vibration energy content is the same,the larger the peak value of modal function is,the larger the peak response of the structure is,the lower the dynamic reliability of the structure is,and the structure is unsafe.