Exact Solutions Of Random Response And Earthquake Action Calculation Of The General Linear Viscoelastic Dissipation Structural-systems

In order to study the brace-general linear viscoelastic dissipation structural-systems in response to seismic excitation and the calculation methods of earthquake action based on seismic codes,the stochastic seismic responses of SDOF and MDOF structural-systems with brace-general linear viscoelastic dampers are studied systematically.Firstly,considering the influence of brace and the most accurate integral model of the general linear viscoelastic damper is adopted in this paper.By using Laplace transform method,the constitutive model of damper is modified,and its equivalent equilibrium stiffness and relaxation function is obtained in the Laplace domain.The brace-general integral damper model is completely transformed into an equivalent modified damper model.Secondly,the structural differential-integral dynamic equations are established and the accurate modeling of the brace-general linear viscoelastic dissipation structural-systems are realized.Then,the Laplace transform of the asymmetric dynamical equations of the structural-systems are performed;By using transfer matrix method,the exact solutions in original structural for space displacement and velocity transient responses of the brace and damper as well as overall structure due to arbitrary exterior dynamic loading and initial conditions are obtained.Thirdly,in order to verify the correctness of the transfer matrix method to solve the seismic response of the brace-general linear viscoelastic dissipation structural-systems.The SDOF and MDOF structural systems are tested based on the complex mode method.For a SDOF structura-systems,the brace-Maxwell model,the GHM model and the brace-general Maxwell model are used respectively;For a MDOF structural-systems,the brace-Maxwell model is used,and the damper's force are treated with two kinds of methods.The structural displacement and velocity transient responses of the brace and damper as well as overall structure are exactly the same based on transfer matrix method and complex mode method under the same structural systems above,so as to verify the correctness of the theory.Fourthly,based on the exact analytical expressions of the overall structural transient response obtained by the transfer matrix method.The analytical expressions for the variance of the structural responses under three kinds of stationary seismic excitation and three kinds of non-stationary seismic excitation are obtained.Analytical method for the analysis of stationary and non-stationary seismic responses for SDOF and MDOF dissipations tructural-systems with the brace-general linear viscoelastic dampers are established,and four calculation examples are given.Lastly,by using integral transform method,the overall structural transient responses for SDOF and MDOF dissipation structural-systems are decomposed into the linear combination of the response variances of first-order and two-order standard oscillator.Then,the square of the extreme value of the structural responses for SDOF and MDOF dissipation structural-systems are decomposed into the linear combination of the square of the responses' extreme value of first-order and two-order standard oscillator.By using the stationary white noise model,the ratio-coefficient of the extreme value of responses of the first-order standard oscillator and the two-order standard oscillator is established.So the maximum response of the structures is expressed by the response of the two-order standard oscillator.Finally,based on earthquake response spectrum of seismic code of China,the approximate analytical solution of earthquake action values of the brace-general linear viscoelastic dissipation structural-systems are obtained,and two calculation examples are given.