Numerical Study On Friction Coupling Effect When Shear Keys Of Friction Pendulum System Are Sheared Asynchronously

When the friction pendulum system(FPS)and shear keys in the bridge structure work together to resist the ground motion input by inclination(not 45 °),it will lead to the shear key in XY direction being sheared asynchronously,so that the friction pendulum system will have a violent change of direction curve movement on the sliding surface with the ground motion,and there is a strong plane friction coupling effect in the whole process.Therefore,it is of great significance to understand the influence of friction coupling on the vibration and isolation performance of friction pendulum system under earthquake.In this paper,a Spring-Viscous damping-Coulomb friction plane isolation system with XY shear keys is constructed.The system can decouple the friction coupling in FPS under earthquake,and realize a more accurate two-dimensional equivalent simulation of FPS.In order to study the effect of friction coupling on the vibration and isolation performance of FPS under earthquake,based on the system,the time history response of FPS under different parameters is calculated by self-made program in this paper.Finally,the collision correction formula of the shear key of FPS is introduced into the self-made program to realize a more accurate calculation of the structural response when the sliding block of the FPS collides with the shear key under earthquake.The main research work of this paper is as follows:(1)In this paper,the equivalent bilinear model of friction is abandoned,and the Spring-Viscous damping-Coulomb friction plane isolation system with XY shear keys is constructed.Based on the mechanical analysis of the system,using the characteristic that the friction force in FPS is a constant 8)2),the variation process of friction force and resultant force on FPS in any calculation time step is expressed by circle making method.Finally,according to the step-by-step integration method,the time history response of the system under earthquake is calculated by programming in Tcl/Tk language.The self-compiled program can effectively realize the decoupling calculation of friction coupling in FPS.Therefore,according to the program,the influence of friction coupling on the vibration and isolation performance of FPS can be effectively studied.(2)By comparing and analyzing the time history response of the equivalent model of FPS in three cases,(XY shear keys sheared simultaneously;XY shear keys sheared asynchronously with = 0;XY shear keys sheared asynchronously with ≠ 0;),it can be found that when the XY shear keys of FPS is sheared asynchronously,on the one hand,it will change the motion state of the support and bring the influence of friction coupling,on the other hand,it will make the acceleration of the structure sudden change at the time of shear keys sheared.When the shear force of XY shear key is small,the plane friction coupling will play a leading role,reducing the maximum acceleration of the structure.At the same time,the friction coupling effect caused by the different shearing of the XY shear key of FPS will increase the maximum relative displacement of the structure.This amplification effect needs to be considered in the seismic reduction and isolation design of the structure with small PGA.(3)In this paper,the variation law of the maximum relative displacement of the structure with the spring stiffness coefficient,damping constant and friction coefficient under friction coupling is analyzed in detail,so as to find the optimal parameter design of the isolation system under the friction coupling.The results show that the friction coupling effect will amplify the relative displacement peak of the system,and the smaller the PGA is,the more significant the amplification effect is;The action mechanism of friction and viscous damping is different,but with the increase of friction coefficient or damping constant,the maximum relative displacement of the structure will continue to decrease,and will decrease rapidly first and then slowly.The optimal parameters are obtained at the boundary point of the reduction rate;The increase of spring stiffness coefficient will significantly reduce the relative displacement amplification effect caused by friction coupling,and first decrease rapidly,and then weaken slowly.There is a boundary point value,and this value will not cause resonance.(4)Abandoning the assumption that a pair of shear keys in the same direction(X or Y direction)of the FPS are sheared simultaneously,it is considered that the cutting of the four shear keys of FPS are independent of each other,and the numerical analysis program of the two-dimensional equivalent calculation model of the FPS described above is collided and corrected,Thus,the accurate simulation of each collision between FPS and the shear key under earthquake is realized,and the impact of the collision on the response of FPS,when shear keys are sheared asynchronously,is accurately studied.The results show that the increase of spring stiffness will weaken the displacement amplification of FPS caused by collision,and the impact of collision on displacement is related to the time of collision.When the spring stiffness is too large,the resonance phenomenon will be destroyed by frequent collision,so as to reduce the displacement response of the structure.Similar to the effect of friction coefficient,when there is damping effect,it will also weaken the impact of collision on structural displacement.However,when friction plays a dominant role in the stress of the structure,the collision will raise or lower the displacement time history curve of the structure,and the amount of change is determined by the velocity increment caused by the collision and the duration of the velocity increment.