Flow of magnetorheological (MR) fluids in dampers is investigated. The MR fluid flows through narrow passages in the damper subject to a magnetic field applied across the passages. The inverse problem of the determination of the required constitutive properties of the MR fluid together with the corresponding flow pattern for the efficient damping of a given load is solved. The fluid is modeled as a Bingham plastic with time-varying yield-stress. Flow is governed by the continuously adjustable constitutive parameters of the MR fluid which are determined to generate variable resistance to flow to dampen the selected load efficiently. The method developed leads to the determination of the magnetic field variation necessary to achieve a specific displacement of the piston in the damper. The governing equations are solved for any time history of the dimensionless yield stress of the fluid. Relationships that correlate damping load and magnetic field time variations are obtained. The analytical tools developed are helpful in damper design.

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