Elucidating design and functional dependence of eddy-current resonators in vibrating elastic metamaterials

Electromechanically coupled metamaterials and systems offer tremendous freedom in the design of adaptive and tunable structures for elastic wave manipulation and control. Electrical circuits are readily reconfigurable, facilitating rapid adjustment of host structure dynamics. By exploiting eddy-current induced Lorentz forces, this research develops a theoretical basis for the design and analysis of fully non-contact local resonators for vibration suppression via transmission stopbands. Based on magnetic induction, two-way electromagnetic coupling is achieved between vibrational accelerations and electrical current. To provide tunability and account for dissipative losses, analog impedance converters are synthesized into electrically tunable LC-oscillators that shape the elastodynamic response without the need for real-time control. A physics-based lumped parameter model is derived to quantify the electromagnetic coupling mechanics, capturing frequency dependence and sensitivities to geometric placement, lift-off distance, host conductivity, damping, and high-order perturbations. Parametric studies emphasize design trade-offs, providing a practical and interpretable framework for prediction and tuning, while elucidating operational constraints and optimal performance criteria. Experimental demonstrations complement the theoretical work, highlighting practical feasibility while underscoring implementation challenges. The results offer key insights and technical contributions on non-contact eddy-current resonators, with relevance to emergent fields in tunable electroelastic metamaterials, mechatronic system integration, and vibration mitigation and control.