The influence of the target earthquake design level on the dynamic response of damped structures

This work investigates how the energy dissipation properties of a structure equipped with nonlinear commercial viscous dampers, designed for a specific target seismic level, are influenced by the variation in the earthquake intensity level, thus deviating from the reference design condition. In this preliminary investigation, Single-Degree-Of-Freedom (SDOF) systems are considered. First, the dynamic response of a nonlinearly damped SDOF system subjected to harmonic excitation is investigated to derive the analytical relationships between the nonlinear damping coefficient, the equivalent damping ratio, the Input Scaling ( IS ) factor, the Output Scaling ( OS ) ratio, and the damping reduction factor. Then, the analysis is extended to SDOF systems subjected to earthquake ground motions. Numerical simulations are carried out through nonlinear time-history dynamic analyses varying the intensity of the base earthquake input. The results indicate that, for SDOF systems under harmonic input, when OS is smaller than 1, the equivalent damping exhibits a marked increase as input intensity decreases, whereas for OS larger than 1, damping decreases with higher input. Forcing frequencies lower than the natural frequency of the system increase the equivalent damping, whereas higher frequencies reduce it. Under seismic input, nonlinear dampers are more effective for IS smaller than 1 and less effective for IS larger than 1. The results, whose quantitative validity is limited to SDOF systems and to a specific earthquake record in the case of seismic input, may provide useful qualitative insights for the preliminary evaluation of dampers’ effectiveness under multiple seismic intensity levels, as typically required in modern Performance-Based and Resilience-Based Seismic Design approaches.