Non-stationary Seismic Response Analysis Of Linearly Viscoelastic Damped Isolated Structure

In order to analysis seismic response and design method of energy dissipation isolated structure which uses the general linear viscoelastic damper model with support based on response spectrum.The modal superposition analytical solutions of the whole structure's non-stationary random seismic response as well as the transient response of the linear viscoelastic damper due to arbitrary exterior forcing loading and initial conditions in time-domain are systematically studied.Firstly,an equivalent constitutive relation is set up to the general linear viscoelastic damper with horizontal support.The integral-differential equations of the structure,which the upper structure of the energy dissipation isolated structure is expanded according to the initial N order vibration mode,are obtained.The extended-order complex modal method has some problems,such as the corresponding relationship between the original space and the extended-order space in the structure is unclear,many problems with extended order variables and low computational efficiency.Non-step-transfer matrix method is used to directly obtain the transient response analytical solutions of the general linear viscoelastic dampers' force and force rate as well as the whole system's displacement and velocity.Then,based on the non-stationary characteristics of actual earthquake comprise amplitude and frequency non-station.Using the frequency domain analytical method obtained the non-stationary mean square response of the general linear viscoelastic dampers' force and force rate as well as the whole system's displacement and velocity under separable or non-separable modulated filtered white noise earthquake excitation,Conte and Peng proposed fully non-stationary earthquake excitation.Using the time-domain analytical method obtained the explicit closed-form non-stationary mean square response of the general linear viscoelastic dampers' force and force rate as well as the whole system's displacement and velocity under the unit step modulated non-stationary,a general form of non-stationary as well as the full non-stationary seismic excitation.The analysis of the non-stationary mean square response of the general linear viscoelastic dampers' force and force rate as well as the whole system's displacement and velocity are attributed to the analysis of the eigenvalues,eigenvectors and standard first-order oscillatory system's responses in the original space.Moreover,combining the non-orthogonal mode superposition exact solutions for the energy dissipation isolated structure by the transfer matrix method and the virtual excitation method,the non-stationary random seismic response of the general linear viscoelastic dampers' force and force rate as well as the whole system's displacement and velocity under the arbitrary modulated non-stationary seismic excitation are solved rapidly.When the traditional sports equations are solved,this way can avoid some problems,such as matrix inversion,inverse matrix does not exist,calculating the index attributes to the loss of calculation accuracy and numerical instability.Finally,by Monte Carlo simulation,the separable or non-separable modulated non-stationary stochastic seismic excitation are proved to be solved by the method of non-expandable transfer matrix.Using the transfer matrix to obtain the analytical solutions of the structure,then combining the pseudo excitation method to solve the transient response of the linear asymmetric frequency dependent structure under the arbitrary modulated non-stationary seismic excitation is also verified.