Study On The Analytical Method Of Random Response And Earthquake Action Calculation Of The General Integral Viscoelastic Damping Structure

In order to study the viscoelastic energy dissipation structure in response to seismic excitation and the calculation methods of earthquake action based on seismic codes, this paper adopts the general integral constitutive model of viscoelastic material and also adopts integral differential hybrid unsteady equations of motion to model a general viscoelastic damping structure accurately.Firstly, based on the Laplace transform, this paper adopts transfer matrix method to achieve accurate decomposition of dissipative structure equation of motion in the non-expanding order space, and attributes the complex solution problem of unsteady structures’ transient response to the analysis of the structure eigenvalue and eigenvector, thus the analytical expressions of the transient response of displacement and the transient response of speed under a non-zero initial structure conditions are obtained. The traditional expanded-order complex modal method for energy dissipation structure with general Maxwell viscoelastic damper is improved in this paper, and the reduced-order complex modal method is presented. Relationship between the primitive equation eigenvalues including eigenvectors and the expanded-order motion equation around complex model vector is also established. This method simplifies the calculation process, giving the modal vectors a clear physical meaning. Based on the energy dissipation structure with general Maxwell viscoelastic dampers, analytic expression of the structural transient responses is obtained which is entirely consistent with the transfer matrix method, verifying the correctness and applicability of the transfer matrix method. And the analytical formula of damper transient response is obtained for the first time..Secondly, in order to study the random response of energy dissipation structure, this paper derives the structure’s analytical expressions of random response variance under stationary and non-stationary seismic model activities based on energy dissipation structure with general integral viscoelastic dampers.Finaly, in order to study the value-methods of structural response design value based on earthquake seismic code, displacement and speed variances of the energy dissipation structure are decomposes to the linear combination of the response variance of first-order and second-order standard oscillator. Based on the stationary white noise model, the ratio of response variance between first-order and second-order standard oscillators is obtain approximately, which makes the structural response design value a function containing only with the square of displacement and velocity spectrum of second-order standard oscillator. Thus, the approximate design value of structural response and the analytical method of the corresponding approximate values of seismic load can be obtained.