Random Response Analysis Of Base-isolated Structures With Limit Protection Device Based On Probability Density Evolution

With the progress of social science and technology,the technology of seismic isolation has been greatly developed.At present,seismic isolation technology has been widely used in engineering structures due to its advantages of simple mechanical model,clear mechanism and obvious damping effect.According to the principle of isolation,the isolation layer has a large horizontal displacement due to its small horizontal stiffness under the earthquake,which dissipates the seismic energy and guarantees the safety of the superstructure to achieves the isolation effect.However,earthquakes have a strong randomness.Earthquakes with excessive fortification intensity occur from time to time.Under the action of strong earthquakes,the horizontal shear displacement of the rubber isolation bearing is large,which may even exceed its failure displacement,resulting in the failure of the isolation layer and the overall tilt or collapse of the superstructure.A limit protection device is adopted for the seismic isolation layer to limit the displacement of the seismic isolation layer within the allowable range,thereby providing a second guarantee for the safety of the structure.In addition,the physical parameters of the engineering structure also have obvious randomness.Under static load,the variability of the structural response and the variability of its physical parameters are usually in the same order of magnitude,but under random dynamic external loads,due to random excitation the coupling effect with random structural parameters often causes the variability of the nonlinear response of the structure to change by several orders of magnitude,which indicates that the deterministic analysis for a strongly nonlinear vibration isolation structure system has not fully reflect the structure of the mechanical behavior during the service.In this context,the probability density evolution method is used in this paper to analyze the random response and reliability of the base isolation structure and the base isolation structure with finite position protection devices.The main research contents are as follows:(1)The basic principle of the probability density evolution method is studied,and the numerical solution process of the generalized probability density evolution equation is analyzed,including the generation of representative point sets and initial probabilities,the deterministic dynamic analysis of the structure,and the TVD difference scheme solution.A physical random function model of ground motion that can reflect the probability information of the ground motion process is introduced.Based on these theoretical foundations,all probabilistic information of the structural random linear and nonlinear response can be obtained.(2)It was established that an equivalent Matlab multi-mass point simulation model based on the Etabs model.Assuming that only the external loads of the earthquake were random,the linear random response analysis of the earthquake-resistant structure and the base-isolated structure under the fortification intensity was performed through probability density evolution method.The results show that the probability density evolution method can well analyze the response of the structure under the action of earthquake.(3)A new type of flexible limit protection device is used to solve the problem of excessive displacement of the isolation rubber bearing under the action of rare earthquakes.The restoration force model of the device is simulated by the "triangle" elastoplastic model.To further study the nonlinear random response of the base-isolated structure and the effect of the limit protection device on the base-isolated structure under the action of rare earthquakes,it is assumed that the structural isolation rubber support parameters and seismic excitation are both random,and the Simulink module is used to analyze the deterministic dynamic response of the base isolation structure and the base isolation structure with limit device under the action of multiple seismic waves,and the probability density information of the displacement response of the two structures is given.(4)Using the probability density evolution method of extreme value distribution,after obtaining the extreme value of displacement of the structure under the action of rare earthquakes,by constructing a virtual process related to the extreme value and using the TVD difference format to solve,the limit base isolation can be obtained Reliability of structure and infinite base-isolated structure.