Stochastic Earthquake Response And Earthquake Action Calculation Of Two Degrees Of Freedom Generalized Maxwell Damper Energy Dissipation Structures

In order to research linear viscoelastic damper energy dissipation structure withsupport, in this paper, the accurate generalized Maxwell viscoelastic damper modelis introduced and used.the stochastic seismic response of damper energy dissipationstructure is researched.And approximate analysis method of earthquake action isstudied. Firstly, the influence of supporting stiffness on vibration attenuation andstochastic response of damper energy dissipation structure are introduced.Theconstitutive relation of viscoelastic damper with support is described.The Maxwelldifferential constitutive model and the generalized Maxwell differential constitutivemodel of viscoelastic damper are elaborated.Exact analytic method of the stationary response of single and two degree offreedom model of generalized Maxwell viscoelastic damping structure areresearched.By using the generalized Maxwell differential constitutive model and thewhite noise stochastic ground motion model, the structure is analysed in detail.Byusing the extended order method, the two order frequency equation of motion of thestructure and the generalized Maxwell differential type constitutive equation arechanged into first-order linear time invariant state equations.The complex modalmethod is used to decouple precisely in order to get the precise value of complexmodal response, which can accurately get the random seismic response of dampingenergy dissipation structure. Then the stationary response variance is obtained by timedomain method.And in the frequency domain, the structural response variance isprecisely expressed as a linear combination of displacement response variance asfirst-order standard vibrator and random response variance of two order standardvibrator.At the same time, the total response of negative real eigenvalues, conjugatecomplex eigenvalues and their mutual coupling are researched.And the preciseexpression is obtained.Then the stationary response maximum values of structure are expressed as thecombination of the accurate maximum response that first-order standard vibratorproduced and two order standard vibrator produced.And the proportion relationshipbetween them is determined through analysis.The relationship between designresponse spectrum and two order standard vibrator maximum response is used.Byusing the acceleration response spectrum of two order standard oscillator, themaximum response generated by two order standard vibration is calculatedaccurately.According to the white noise random vibration model, the ratio of the totalmaximum response of first order standard vibrator and two order standard vibrator is get approximately. So the approximate analysis method of response andcorresponding design method of seismic load value are get.Finally, an example isgiven to verify the correctness of these analysis methods. The influence of change ofdamping force on response of complex conjugate eigenvalues is analyzed.And thechange trend of response produced by the coupling of negative real eigenvalues andcomplex conjugate eigenvalues is analyed.Thus the engineering design personnel canmaster the analysis method with physical meaning easily.Then this method is appliedwith the seismic theory for seismic design of building structures.