Harvesting energy from the sloshing motion of ferrofluids in an externally excited container: Analytical modeling and experimental validation

When a container carrying a magnetized ferrofluid is subjected to external mechanical stimuli, the sloshing motion of the magnetized ferrofluid generates a time-varying magnetic flux, which can be used to induce an electromotive force in a coil placed adjacent to the container. This process generates an electric current in the coil, and therewith, can be used to transduce external vibrations into electric energy. In this article, we develop a nonlinear analytical model, which governs the electro-magneto-hydrodynamics of an electromagnetic ferrofluid-based vibratory energy harvester. Using perturbation methods, we obtain an approximate analytical solution of the model for a case involving primary resonance excitation of the first mode and a two-to-one internal resonance between the first two modes. This occurs when the external excitation is harmonic with a frequency close to the fundamental sloshing frequency and when the second modal frequency is nearly twice the first modal frequency. Theoretical results are compared to experimental findings illustrating very good qualitative agreement.