One-way sound propagation via spatio-temporal modulation of magnetorheological fluid

This manuscript details the possibility of achieving one-way sound propagation using a smart fluid such as magnetorheological fluid (MRF) by subjecting it to a spatio-temporally varying magnetic field. The local speed of sound in MRF is dependent on applied magnetic field as demonstrated in several experimental works and this property of MRF has been leveraged, in this work, to induce one-way bandgaps. Initially, a general wave equation pertaining to fluid with space-and-time-varying material properties was derived. Assuming plane wave propagation in one dimension, an approximate Floquet solution was imposed and the dispersion relationship was obtained. A comprehensive finite element analysis was conducted and good agreement was noted between the numerical and theoretical dispersion relations. It was concluded that space-time periodic modulation of fluid density and local sound speed is necessary to induce asymmetry in the band diagram around the ω axis. The feasibility of real-world implementation using MRF has been discussed. A parametric study detailing the effect of viscosity on the one-way bandgaps has been undertaken. It was found that one-way bandgaps formed at relatively lower frequencies are more robust to viscous corruption. A real-world implementation may be feasible if the viscosity of MRF is less than 3000 Pa-s.