Nonlinear Random Dynamic Response And Reliability Analysis Of Isolated Curved Girder Bridge Under Multidimensional Excitation

Curved girder bridges can overcome complex terrain and ground conditions,meet the overall continuity of the route,and have smooth architectural lines.Therefore,they are widely used in urban elevated,overpass and highway projects at home and abroad.However,because of the irregularity of the superstructure of the curved beam bridge,the structure will appear "bending-torsion coupling" phenomenon in the earthquake process,making it more serious than the linear bridge in earthquake disasters.Therefore,analyzing the nonlinear random dynamic response and reliability of seismically isolated curved girder bridges under rare earthquakes is of great significance for studying the seismic performance of curved girder bridges.Based on the complex mechanical characteristics of seismically isolated curved beam bridges,this paper uses MATLAB software to carry out a series of researches on nonlinear random dynamic response,vibration control and dynamic reliability of seismically isolated curved beam bridges.The specific research content is as follows:(1)In this paper,based on the existing dual-particle six-degree-of-freedo m simplified model,the classic Bouc-Wen model is used to simulate the hysteresis characteristics of the seismically isolated curved beam bridge during rare earthquakes.The nonlinear dynamic equation considering the eccentricity of the upper structure of the curvilinear isolated girder bridge was established,and the Runge-Kutta method was used to solve the nonlinear dynamic equation.The effects of ground motion incident Angle,radius of curvature and bearing yield ratio on the nonlinear dynamic response of the curvilinear isolated girder bridge under rare earthquake were analyzed.(2)Aiming at the problem that the seismic response of the structure under random excitation is also a random process,with the help of random vibration theory,a nonlinear random vibration equation considering the eccentricity of the upper structure of the seismically isolated curved beam bridge is established.After the random equivalent linearization of the equation,Euler ’s formula is used to transfor m the virtual excitation into a simple harmonic external load,combined with the fine integration method,to derive the special solution fine integration format under different modulation functions.These integration schemes are used to solve the response at each moment,and the displacement,velocity power spectral density and time-varying variance of the seismically isolated curved beam bridge under multi-dimensional stationary and non-stationary random excitation are obtained.The analysis considers the influence of the steady and non-stationary random excitation of the torsion component on the random dynamic response of seismically isolated curved girder bridges with different bridge deck widths,curvature radii and bearing yield ratios.(3)Under rare earthquakes,elasto-plastic deformation of seismically isolated curved beam bridges will occur.In order to effectively suppress the displacement o f excessive beams and supports in seismically isolated curved beam bridges,a semi-active control strategy is adopted to ensure its safety.Establish a nonlinear vibration control equation for a seismically isolated curved beam bridge,and then equivalently linearize the equation based on the zero hysteresis displacement condition to obtain the optimal control force of the sequence optimal control under definite excitation and random excitation.Based on the classical linear optimal control(COC)and sequential optimal control(SOC),the seismic response of the seismically isolated curved beam bridge under definite seismic excitation,stationar y and non-stationary random excitations are respectively analyzed for vibration control,and compared and analyzed the dynamic response of a seismically isolated curved girder bridge under three control states.(4)In order to objectively evaluate the seismic performance of curved girder bridges,the loss caused by the earthquake is minimized.From the perspective of reliability,establish the functional state function of the substructure of the seismic isolation curve beam bridge and the seismic isolation support under the action of rare earthquakes.Based on the theory of first transcendence failure,the influence o f different bridge deck width,radius of curvature and yield ratio of the support on the dynamic reliability of the isolated curved girder bridge under controlled and uncontrolled conditions under steady and non-stationary random excitation is analyzed.