Improved Stochastic Linearization Methods for Structures with Nonlinear Eddy Current Dampers Considering Non-Gaussian Distributions

Eddy current dampers (ECDs), which employ magnetic induction to produce eddy current damping for energy dissipation, demonstrate superior sensitivity and durability in comparison to traditional viscous dampers. However, the inherent, velocity-dependent nonlinearity of ECDs poses significant challenges in research and engineering implementations. The present study addresses this challenge by exploring the stochastic linearization of ECDs, innovatively incorporating the non-Gaussian distribution of velocity responses. Central to our analysis, we proposed four closed-form expressions for the equivalent damping ratios of ECDs, derived from both Gaussian and non-Gaussian distributions. This achievement is facilitated by the utilization of the statistical linearization technique (SLT), which integrates both force-based and energy-based equivalent criteria. To validate the accuracy of these expressions, Monte Carlo simulation (MCS) was employed. Our results demonstrate that, regardless of soil conditions and velocity distributions, the force-based criteria, in most cases, outperform the energy-based criteria in assessing the stochastic linearization of ECDs. Notably, in scenarios where ECD nonlinearity is prominent, the probability density of the exact velocity response of ECDs in firm soil exhibits a significantly steeper profile near zero, resembling an exponential-like distribution more closely than the Gaussian distribution. Conversely, in soft soil conditions, the actual velocity distribution lies intermediate between Gaussian and exponential-like distributions. Additionally, a series of parameter studies were conducted, further revealing that the force-based Gaussian SLT method offers the highest accuracy in soft soil and firm soil with critical velocities exceeding 0.05[Formula: see text]m/s. In contrast, the force-based non-Gaussian SLT method proves to be the more precise approach in firm soil with critical velocities below 0.05[Formula: see text]m/s.