Study On The Coupling Effect Of Damping Nonlinearity And Ground Motion On Structural Seismic Response

The nonlinear response characteristics of structures under seismic action are the basis of seismic analysis and collapse prevention design.When the structural mass,stiffness and connection are changed due to damage and other reasons,the structural damping will be changed.Due to the complexity of nonlinear calculation,the study of nonlinear time history under seismic action is more focused on the nonlinear effect of stiffness,but less on the nonlinear effect of damping.The energy dissipation of structures under earthquake mainly depends on the damping effect.The damping mechanism of building structure is very complex,which will be accompanied by damage with time,and has a non-linear nature.Based on this,this paper mainly studies the seismic response characteristics of nonlinear damping structures under ground motion with the help of two algorithms.The parametric characteristics of nonlinear viscous damping are analyzed systematically.The perturbation degradation characteristics of nonlinear damping are analyzed by using Taylor series expansion and finite difference scheme.Based on four typical ground motions of four kinds of sites,the displacement time history responses of single-degree-of-freedom and multi-degree-of-freedom nonlinear damping structures under different ground motions are calculated and analyzed respectively.Two different numerical methods are used for comparative calculation.The first is to use the idea of secant approximation to transform the nonlinear problem into a linear one,and then use Newmark-β method to solve the differential equations of motion of the single-degree-of-freedom system.In the second method,Runge Kutta method is used to solve the nonlinear differential equations of motion in the single-degree-of-freedom system.The displacement time histories of structures under four typical ground motions are calculated by using the two methods,and the calculation errors of the two methods under different ground motions are compared and analyzed.Under the same ground motion,the difference between the results of the two algorithms will increase with the increase of the degree of damping nonlinearity.Under the same algorithm,the error of the result will also increase with the increase of the degree of damping nonlinearity.Therefore,the uncertainty of structural nonlinear seismic response analysis caused by nonlinear damping on structural seismic response analysis needs to be further clarified.The displacement response of the single-degree-of-freedom nonlinear damping system under the different ground motions decreases gradually with the increase of damping nonlinearity.However,the variation of the maximum displacement response of the multi-degree-of-freedom nonlinear damping system with damping nonlinearity is obviously related to the characteristics of seismic action.Under the action of ground motion of type II and III sites,the displacement response decreases with the increase of damping nonlinearity.Under the action of ground motion of type I site,when the damping index is less than 0.5,the displacement response decreases with the increase of nonlinearity,but when the damping index is greater than 0.5,it shows the opposite trend.Under the action of the ground motion of IV site,the displacement response of the stronger damping nonlinearity is larger than that of the weaker damping nonlinearity.Therefore,the coupling effect of ground motion characteristics and damping nonlinear effect on structural response is an important part of structural seismic response and failure analysis.