Stochastic Response Analysis Of Weak Nonlinear Structures With Viscoelastic Dampers Under Biaxial Earthquake

In order to study the random response problems of weakly nonlinear structure of Viscoelastic dampers with braces under Bi-directional Earthquake Action.in this paper,through the analysis of Bi-directional Earthquake Action,and the principle of structural vibration control,comparative analysis of Kelvin model,Maxwell model,the standard linear solid model.through the analysis of the equivalent linearization method,and using the basic perturbation method,the feasibility and superiority of the structural response is verified.The establishment of transformation between the damper and the original damper with the performance parameters of brace,then The damper translate into a new integral type damper without brace.Based on The constitutive relation of general integral type damper and the equivalent linearization method,the equations of motion of a SDOF nonlinear structure of a generalized Maxwell damper with brace are established.Conclusions are as follows:1.Based on the stochastic averaging method,General analytic expression of the joint probability density function and Statistical properties of displacement and velocity response of a SDOF nonlinear structure of a generalized Maxwell damper with brace are established.the equations of motion equivalent structure of a SDOF nonlinear structure of a generalized Maxwell damper with brace under Bi-directional Earthquake Action are obtained.The displacement response variance is decreases with the increase of the damper coefficient within a certain range By the equation of motion of the equivalent structure.2.Based on the characteristics of non expansion of energy dissipation structure,General analytic expression of Random response of displacement and velocity in time domain of a SDOF nonlinear structure of a generalized Maxwell damper with brace are established.Based on Analysis of eigenvalues and eigenvectors between non expanded and expanded of energy dissipation structures,the Reduced order analytic expression of Response of order structure is obtained:Displacement response of energy dissipation structure,Speed response of energy dissipation structure,Stress response of damper of energy dissipation structure;on this basis,General analytic expression of Nonstationary covariance function of general random response are obtained.