Stochastic Response Characteristic And Dynamic Seismic Reliability Of Nonlinear Energy Dissipation Structures

At present,there is no productive method for the random seismic response of weak nonlinear energy dissipation structure with supporting brace and viscoelastic damper at home and abroad.In order to study the random response problems of weakly nonlinear structure of viscoelastic dampers with braces under the random earthquake action,this paper uses structural vibration control principles and nonlinear random vibration theory,combined with Kelvin viscoelastic damper considering the effects of supporting brace.The following research was made:Based on the stochastic equivalent linearization method and the equivalent damping formulas,the numerical solution and the analytical expression of the random response of the weakly nonlinear SDOF structure with Kelvin viscoelastic damper and supporting brace are derived.Through a typical example,it is verified that the Kelvin viscoelastic damper with brace has a good shock absorption effect on the Duffing system.At the same time,the impact of the brace stiffness on the shock absorption effect of this type of nonlinear structure is analyzed.The greater the brace stiffness is,the better the shock absorption effect is.Based on the FPK equations、the stochastic equivalent linearization method and the equivalent damping formulas,the numerical solution and the analytical expression of the random response of the weakly nonlinear SDOF structure with Kelvin viscoelastic damper and supporting brace and the joint probability density function of structure are acquired.The deviation of the displacement response calculated by the FPK equations and the stochastic equivalent linearization method are compared.And the research achievement shows that the calculating precision based on the FPK equations has higher accuracy than the stochastic equivalent linearization method.Based on the equivalent Duffing system method、the FPK equations、the stochastic equivalent linearization method and the equivalent damping formulas,the numerical solution and the analytical expression of the random response of the weakly nonlinear SDOF structure with Kelvin viscoelastic damper and supporting brace are derived.Through a typical example,it is verified that the Kelvin viscoelastic damper with brace has a good shock absorption effect on the Van der pol system.The deviation of the displacement response calculated by the FPK equations and the stochastic equivalent linearization method are compared.Besides,the difference between the standard deviation of the displacement response calculated by two analysis methods is changed in the range of 3%.The two methods are applicable to general weak nonlinear structures containing viscoelastic dampers.