Random Seismic Response Analysis Of General Integral Viscoelastic Dampered Isolated Stuctures With Support

In this paper,the transfer matrix method and stochastic averaging method are respectively used to study the response under seismic excitation and earthquake action calculation based on seismic codes of energy dissipation of base isolated structures,which uses the general integral viscoelastic damper model with support.First of all,the viscoelastic integral constitutive relation is used to model the exact dynamic integral-differential equations of the energy dissipation of base isolated structures.The displacement of the superstructure is expanded according to the first Nth modes,and the structure with the integral-differential equations of the structure with the first Nth modes are obtained.The transfer matrix method is used to obtain the transient response analytical expressions of the displacement,velocity and damper's force of the structure subjected to arbitrary seismic excitation in the non-expanded original space.Based on 3 kinds of stationary and 9 kinds of non-stationary seismic excitation model,the analytical solution of the stationary and non-stationary mean square response of the displacement,velocity and stress response of the damper of integral viscoelastic damping energy dissipation isolated structure with support is obtained.Then,by using the stochastic averaging method,the integral-differential equations of the dissipation isolation structure are transformed into differential equations of the second order equivalent constant system,the equivalent system is solved by using transfer matrix method,and the approximate response analytical solutions of displacement and velocity are obtained.And random response variance analytic expressions of integral viscoelastic energy dissipation isolation structure with support is obtained for the stationary and non-stationary seismic excitation models.Based on the results of the transfer matrix method,the stochastic averaging method is compared with the modal strain energy method,it is found that the stochastic averaging method has higher accuracy.Finally,under the excitation of white noise,through the identity transform,the variances of the structural response obtained by the transfer matrix method and the stochastic averaging method are decomposed into a linear combination of the first order and the second order standard oscillator response variance.Then,the square of the structural response extremum is decomposed into a linear combination of the first order and the second order standard oscillator extreme response variance.According to the corresponding relationship between the extreme response and the response variance of a series of standard oscillator,the accurate and approximate analytical method for the extreme value effect of the normalized response spectrum and the equivalent static seismic action value of the energy dissipation isolation structure are established.