The dynamic behaviour of conductive beams subjected to magnetic fields involves complex interactions between mechanical motion and induced electromagnetic forces. This study introduces a coupled computational approach that captures the mechanisms of eddy current damping and their role in vibration attenuation and bending-torsion coupling of thin, non-magnetic conductive beams. The structural response is modelled using finite elements that include bending and torsional degrees of freedom, while the electromagnetic effects generated by motional induction are evaluated through a finite difference formulation. The resulting velocity-dependent electromagnetic forces are integrated directly into the dynamic equations of motion, resulting in a symmetric but non-proportional damping matrix governing both energy dissipation and cross-coupling between vibration modes. The proposed formulation is further validated against experimental data, confirming its ability to accurately reproduce the observed dynamic response. Frequency- and time-domain simulations reveal that increasing magnetic field magnitude enhances vibration attenuation, and that bending-torsion coupling arises only when magnetic fields are oriented in multiple directions. The proposed model provides a systematic means to investigate electromagnetic–mechanical coupling mechanisms in beam-like structures and to predict their dynamic performance under magnetic fields, offering new insights and computational tools for non-contact vibration control in advanced mechanical systems.
Brun et al. (Thu,) studied this question.