Edge-induced nonlinear damping in bilateral-plate eddy-current tuned mass dampers

Eddy current damping is commonly modeled using linear viscous-equivalent formulations. However, for finite-width conductor plates, relative motion between permanent magnets and the conductor causes the electromagnetic interaction region to approach the plate edges, where the effective conducting area decreases, giving rise to a displacement-dependent nonlinear damping mechanism. This paper investigates edge-induced nonlinear eddy-current damping and its influence on dynamic behavior, using a bilateral-plate eddy-current tuned mass damper (BP-ECTMD) as a representative configuration. An analytical model is developed by explicitly accounting for the translating integration bounds associated with finite conductor plates in a magnet-fixed coordinate system. The resulting damping force exhibits a pronounced nonlinear dependence on relative displacement, characterized by a two-stage, S-shaped decay. This behavior is efficiently approximated by a compact logistic-type function suitable for nonlinear dynamic analysis. The analytical predictions are validated against three-dimensional finite-element simulations for different air gap thicknesses, with errors generally below 10%. Nonlinear dynamic analyses show that linearized damping models are adequate only for small vibration amplitudes. At larger displacements, edge-induced effects significantly reduce the effective damping and alter vibration response characteristics. In the numerical example, if the nonlinear BP-ECTMD is designed using the optimal damping coefficient of the linear TMD, its peak structural response reaches 1.655 times that of the linear TMD; after re-optimization, the best nonlinear design is obtained at 1.5 times this damping amplitude, reducing the peak response to 0.968 times that of the linear TMD. These results demonstrate that edge-induced nonlinear damping is an intrinsic feature of plate-type eddy-current dampers and must be explicitly considered in nonlinear mechanical modeling.