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Identical mathematical expressions for viscoelastic and viscous damper-brace components are derived as the function of two fundamental nondimensional parameters. These two parameters are used to investigate the properties of viscoelastic (VE) and viscous (VS) systems by conducting parameter analysis. Usually both VS and VE damper-brace components provide added stiffness and damping to the whole system. The magnitude of the added stiffness and damping depends not only on the damper, but also on the interaction of the damper with other members of the frame. Under conditions of low frequency and stiff brace, the added stiffness provided by a VS damper-brace component is negligible. based on harmonic theory, closed-form solutions for seismic response prediction are presented and are used to determine the optimal design. As an example, the seismic performance of a 10-story steel frame incorporated with VE and VS dampers is studied.

This paper proposes a simplified theory to predict and compare the seismic performance of viscoelastical (VE)- and elastoplastical (EP)- damped passive control systems, and to demonstrate their ability to protect structures during a major seismic event. Closed-form expressions for 'equivalent period' and 'equivalent damping' of these systems are proposed by idealizing them as linear single-degree-of-freedom (SDOF) systems. The expressions are used to clarify and compare the structural parameters, seismic drift, and force for the systems, based on a common high-damping linear spectrum. By extending the SDOF theory, a seismically deficient 14-story steel moment resisting frame (MRF) is upgraded by inserting VE or EP dampers. Extensive three-dimensional multi-degree-of-freedom nonlinear dynamic analyses are performed for the MRF, VE system, and EP system using earthquakes of various intensities. The 14-story VE and EP systems responded as predicted by the SDOF theory. They show much smaller drifts than the original MRF, keep frame members elastic, and protect nonstructural components, even against major earthquakes.