The additional damping ratio (ADR) is an important indicator for evaluating the damping effect of structures with energy-dissipation devices. Most existing methods for determining the ADR require an analysis of the structural dynamic response and complex iterative calculations. An innovative simplified calculation method for determining the ADR of a structure supplemented by nonlinear viscous dampers is proposed. This method does not require the dynamic response of the structure to be calculated and only requires the structural characteristics, excitation frequency, and damper parameters. In this study, several typical calculation methods for the ADR were analysed. Then, a calculation formula for the ADR was derived with consideration of harmonic excitation under the condition where the excitation frequency is equal to the structural natural frequency, without calculation of the structural dynamic response or an iterative process. The effect of the excitation frequency on the calculated value of the ADR with different damping exponents was studied. Accordingly, the response spectrum average period (RSAP) was considered as the excitation period of ground motion to evaluate the excitation frequency, and a simplified calculation method for the ADR considering the effect of the excitation frequency characterised by the RSAP of the ground motion was established. Finally, the accuracy and effectiveness of the proposed method were verified by comparison with ADRs calculated using other methods.
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