Simplified Nonlinear Damping Force Formula for Rotary Eddy Current Dampers and Comparative Hazard Analysis under Seismic Excitation with Fluid Viscous Dampers

Ensuring the robust performance of damping devices during intense vibrations, such as seismic excitation, is crucial for maintaining structural protection. Hazard analysis serves as an effective method for evaluating the reliability of vibration-damping devices installed on structures subjected to vibrations. This study aimed to conduct a seismic hazard analysis comparing the rotary eddy current damper (R-ECD) and the widely used fluid viscous damper (FVD). To facilitate analysis and engineering applications, this study introduces innovative contributions by proposing a simplified formula for estimating the nonlinear damping force of the R-ECD under specific conditions. This formula incorporates two physically significant parameters: maximum damping force ($F_{\max }$) and critical velocity ($v_{cr}$). By doing so, it offers a swift and efficient tool for the intricate calculation of damping force. The accuracy of this estimation formula is validated by testing a large-scale R-ECD with a maximum damping force exceeding 1,500 kN, revealing a remarkable agreement of $\pm 6.8\%$ between the estimated and experimental results. Subsequently, employing stochastic linearization, the equivalent linear damping ratio of single-degree-of-freedom (SDOF) structures with R-ECD and FVD were derived. Leveraging this stochastic linearization, seismic hazard analysis of these two dampers was carried out. The results indicate that R-ECDs exhibit superior reliability in terms of self-limited output force and their ability to handle large strokes, outperforming FVDs. Moreover, the findings confirm that ECDs are particularly well-suited for long-span structures such as bridges, which are prone to temperature-related influences.