Calculation of additional equivalent damping ratio for viscoelastic dampers

Viscoelastic dampers typically introduce both stiffness and damping into a building frame,and thus the design of a energy dissipation system added viscoelastic dampers is more complex than a system added viscous dampers.In this paper,a modal equation of motion will be expressed into state space equation,and then a Lyapunov function is constructed.Assumed seismic response of a structure is random response,a calculation formula of additional equivalent damping ratio for viscoelastic dampers is derived.Energy dissipation characteristic of viscoelastic dampers can be expressed by the damping ratio only.The procedure will simplify the design of energy dissipation added viscoelastic dampers effectively.Compared with the general method,the accuracy of the procedure is adequacy,and the result is conservative.