Equivalent damping of dissipation structures with viscous and viscoelastic dampers

The dynamic integro-differential earthquake response equations of SDOF dissipation structure with supporting brace and viscous and viscoelastic dampers in series are firstly established by employing integral constitutive relations of dampers; Then, by the stochastic averaging method and the equivalence criterion of which all random response characteristics are same in the meaning of stochastic averaging analysis, the analytic formulas of equivalent stiffness and damping of arbitrary linear viscous and viscoelastic dampers with supporting brace are established, which make it possible for the structure analysis to use response spectrum technique; And then , the analytic formulas of equivalent stiffness and damping of generalized Maxwell model dampers and generalized differential model dampers with supporting brace are given. It is verified that the proposed method is effective through numerical comparison for some typical problems.