This manuscript investigates one way sound propagation in Magnetorheological fluids (MRF) using spatio-temporal modulation of the applied magnetic field. One-way propagation of waves in a structure can have potential technological applications such as sound isolation, filtering and echo suppression. Several experimental works in the literature have shown that elastic properties of MRF’s (local speed of sound, in particular) are dependent on the applied magnetic field. Therefore, several fascinating possibilities regarding the manipulation of sound waves in MRF, by tailoring the applied magnetic field, exist.

A effective medium approximation (previously used in literature) is used to analyze sound propagation in a MRF composed of hydrogen-reduced Iron particles suspended in pure glycerine. Floquet-Bloch theory is used to obtain a quadratic eigenvalue problem that gives the band structure as a function of the material and modulation parameters. When the applied magnetic field is allowed to vary only in space, regular bandgaps are obtained as a result of Bragg scattering. In contrast, the temporal variation of the magnetic field to induce a traveling wave like variation of the modulated parameters, breaks the symmetry of the Brilloouin zones and we obtain directional bandgaps. The theoretical band structure is validated by numerical band diagrams obtained using a Finite Element code. This research has important applications in active sound manipulation.

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