Random Seismic Response Analysis Of General Integral Damping Energy Dissipation Structure With Brace

For realizing the modeling of dissipation structural stationary and non-stationary responses under earthquake excitation and earthquake action values based on seismic codes,this paper has studied the constitutive relation of general integral viscoelastic damper model with brace,to solve structural responses,and to determine the equivalent seismic actions by using the transfer matrix method and the improved first-order stochastic averaging method respectively.Firstly,using the precise transfer matrix method to model the viscoelastic integral damper with brace of energy dissipation structure,using Laplace transform of complex function to calculate structural eigenvalues and impulse response function,and using mode decomposition to obtain the generalized displacement and velocity formulas,and using inverse Laplace transform,the analytical expressions of response variances of the displacement,velocity and damping force of the structure are obtained.Secondly,using the approximate stochastic averaging method to transfer the viscoelastic damping force into equivalent elastic force and damping force of average time,transfering the structure into the equivalent system,directly obtaining the frequency and vibration mode,and using the transfer matrix method and mode decomposition,the corresponding eigenvalues and response analysis formulas are obtained.And comparison of these results and results of the modal strain energy method shows the superiority of this method.Thirdly,the integral transform structural responses are decomposed into linear combination of the first-order and the second-order standard oscillator and squared responses are decomposed into the combination of the first-order and the second-order extreme response standard oscillator.Then the approximate analytical expressions based on seismic codes are obtained.Lastly,examples considering stationary and non-stationary responses of the single degree of freedom structure and multi-degree of freedom structure of Maxwell dampers or generalized Maxwell dampers with braces are given based on the stationary and non-stationary seismic excitation models and different supporting stiffnesses having effects on structural responses.The results show that the control effect and the supporting stiffness are closely linked.Finally,verify the consistency of the responses before and after the standard oscillator decomposition,and give the earthquake responses and equivalent seismic actions.