Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Simplified analysis and supplemental damping system design

Investigated is the accuracy in estimating the response of asymmetric one-storey systems with non-linear viscoelastic (VE) dampers by analysing the corresponding linear viscous system wherein all non-linear VE dampers are replaced by their energy-equivalent linear viscous dampers. The response of the corresponding linear viscous system is determined by response history analysis (RHA) and by response spectrum analysis (RSA) extended for non-classically damped systems. The flexible and stiff edge deformations and plan rotation of the corresponding linear viscous system determined by the extended RSA procedure is shown to be sufficiently accurate for design applications with errors generally between 10 and 20%. Although similar accuracy is also shown for the 'pseudo-velocity' of non-linear VE dampers, the peak force of the non-linear VE damper cannot be estimated directly from the peak damper force of the corresponding linear viscous system. A simple correction for damper force is proposed and shown to be accurate (with errors not exceeding 15%). For practical applications, an iterative linear analysis procedure is developed for determining the amplitude- and frequency-dependent supplemental damping properties of the corresponding linear viscous system and for estimating the response of asymmetric one-storey systems with non-linear VE dampers from the earthquake design (or response) spectrum. Finally, a procedure is developed for designing non-linear supplemental damping systems that satisfy given design criteria for a given design spectrum.