An Analytical Model and Parameter Sensitivity Analysis of the Energy Dissipation Ratio for Nonlinear Viscous Dampers Under Seismic Excitation

This study investigates the energy dissipation efficiency of structures equipped with nonlinear viscous dampers under seismic excitation. It aims to address the lack of a clear quantitative relationship between the energy dissipation ratio (the ratio of energy dissipated by dampers to the total seismic input energy), ground motion intensity, and damper parameters by systematically examining the underlying energy dissipation mechanism and parameter influence laws. First, an analytical model for a single-degree-of-freedom (SDOF) system controlled by the nonlinear viscous damper is established based on random vibration theory. An explicit analytical formula for the energy dissipation ratio is then derived by incorporating the statistical properties of the velocity response, which reveals a power-law relationship with the peak ground acceleration (PGA), damping coefficient (C), and damping exponent (α). Subsequently, this analytical model is extended to multi-degree-of-freedom (MDOF) structures using the mode decomposition method, leading to an engineering-oriented approximate formula for the energy dissipation ratio under the assumption of first-mode dominance, with its applicability conditions specified. Finally, a six-story reinforced concrete frame is employed as a numerical case study to evaluate the accuracy and engineering applicability of the proposed model through nonlinear time history and sensitivity analyses under various damper parameter combinations. The results indicate that PGA, C, and α all have a significant impact on the energy dissipation ratio and structural response, with C exerting a more direct influence on the overall energy dissipation level. The energy dissipation ratio is demonstrated to be a key performance indicator for damper parameter selection and seismic performance evaluation, providing a theoretical basis and practical reference for the damping design of structures incorporating nonlinear viscous dampers.