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**Sample text**

Based on these results, the hysteresis identification of the MR fluid was performed using the Preisach model. 2) Γ where Γ is the Preisach plane, γ αβ [⋅] is the hysteresis relay, H(t) is the magnetic field, τ y (t) is the yield stress (or shear stress), and μ(α,β) is the weighting function that describes the relative contribution of each relay to the overall hysteresis. Each relay is characterized by the pair of switching values (α,β) with α ≥ β. 6(a). 6(b). It is a modification of a classical relay that has two states, –1 and 1, corresponding to the opposite polarization of a ferromagnetic material.

5), we can determine an explicit formula for the hysteresis in terms of experimental data. 7(b) shows the increasing and decreasing series of an input magnetic field, where Γ+ can be subdivided into n trapezoids Qk. Geometrically, the area of each trapezoid Qk can be expressed as a difference of two triangle areas concerned with T (α k , β k −1 ) and T (α k , β k ), respectively. 8) for decreasing input Numerical implementation of the Preisach model requires experimental determination of T (α k , β k ) at a finite number of grid points within the Preisach plane.

Many types of semi-active MR dampers have recently been proposed to attenuate the vibrations of various dynamic systems including vehicle suspensions. Experimental realization has demonstrated that the unwanted vibrations of application systems can be electively controlled by employing MR dampers associated with appropriate control strategies [17, 18]. The use of an accurate damping force model, which can capture the inherent hysteretic behavior of MR dampers, is a very important factor in the successful achievement of desirable control performance.