Analysis Of Random Response Of An Energy Dissipation Structure With A Maxwell Damper Based On The Stochastic Averaging Method

In this paper, transforms a Maxwell-viscoelastic EDD isolation structure into a second-order approximation- equivalent constant system using the stochastic averaging method, and an earthquake calculation’s analytical method is obtained, its main contents are:1.Converting the frequency domain equations of motion of a Maxwell-viscoelastic damping isolation structure to a second-order equations of motion of an approximate equivalent system using stochastic average method, the second-order approximation equivalent constant system considers coupling of the original structure.2.Converting a Maxwell-viscoelastic damping level isolation structure into three equivalent systems respectively using extended order complex mode method, modal strain energy method and the stochastic averaging method, and through an equivalent system and modal coordinate transformation equations, furtherly, solves its stochastic seismic displacement response’s analytical solutions; Finally, in the case of structural damping coupling and uncoupling, referring to the precise equivalent system based on extended order complex modal method, analyses comparativily the structural displacement response error values obtained by basing on two approximate equivalent systems, which are stochastic averaging method and modal strain energy method, through an example;Therefore,in the uncoupling damping-isolation structure, the calculation precision of the approximate equivalent system based on the stochastic averaging method and calculation accuracy of the approximate equivalent system based on modal strain energy method is basically the same; In the coupling Maxwell-viscoelastic damping isolation structure, the calculation accuracy of equivalent system based on the stochastic averaging method is significantly greater than the one of equivalent system based on the modal strain energy method.3. A second-order approximate equivalent constant system of a Maxwell-viscoelastic damping isolation structure based on the stochastic average method is expressed as displacement and velocity response’s linear combinations of a series of independent single degree of freedom second-order standard oscillators, a unified expression of relatived displacement response, which are the main structure’s each layer ‘s and isolation layer relatived to the ground’s, is abtained, a displacement response variance decomposition of a high-rise Maxwell-viscoelastic damping isolation structure according to the standard vibrator, and its combination coefficients, is abtained; According to a series ofsecond-order standard oscillators’ maximums of displacement and velocity response relationship between seismic acceleration response spectrum, the structural maximum seismic-inter story displacement is abtained. Eventually, a complete analytical method obout the structural earthquake action value based on the stochastic averaging method is established.