Quasi-steady Bingham Biplastic Analysis of Electrorheological and Magnetorheological Dampers GLEN A. DIMOCK,* JIN-HYEONG YOO AND NORMAN M. WERELEY Smart Structures Laboratory, Department of Aerospace Engineering, University of Maryland, College Park MD 20742 USA ABSTRACT: Electrorheological (ER) and magnetorheological (MR) fluids are characterized by an increase in dynamic yield stress upon application of a magnetic field. The Bingham plastic model has proven useful in modeling flow mode dampers utilizing ER and MR fluids. However, certain MR fluids can exhibit shear thinning behavior, wherein the fluid’s apparent plastic viscosity decreases at high shear rates. The Bingham plastic model does not account for such behavior, resulting in overprediction of equivalent viscous damping. We present a Bingham biplastic model that can account for both shear thinning and shear thickening behaviors. This approach assumes a bilinear postyield viscosity, with a critical shear rate specifying the region of high shear rate flow. Furthermore, the model introduces non- dimensional terms to account for the additional parameters associated with shear thinning and thickening. A comparison is made between Bingham plastic and Bingham biplastic force responses to constant velocity input, and equivalent viscous damping is examined with respect to nondimensional parameters. Key Words: Author please supply Keywords ??? INTRODUCTION M AGNETORHEOLOGICAL (MR) fluids and electro- rheological (ER) fluids have been proposed for a wide variety of engineering devices requiring semiactive damping (Carlson et al., 1999). These fluids, demon- strated to be qualitatively similar, are characterized by a field-dependent yield stress (Weiss et al., 1994). Because of their field-dependent properties, ER and MR fluids have been utilized in a number of control studies to reduce transmissibility in civil structures (Spencer et al., 1998; Hiemenz and Wereley, 1999), automotive systems, and other dynamical systems (Sharp and Hassan, 1986; Jeon et al., 1999). This paper will focus on MR fluids, which respond to a magnetic field and have achieved greater commercial success in practical devices than their ER counterparts (Stanway et al., 1996; Jolly et al., 1999). Magnetorheological fluids are known to exhibit a number of nonlinear phenomena. A wide variety of nonlinear models have been used to characterize MR fluids and devices, including the Bingham plastic model (Phillips, 1969), biviscous models (Stanway et al., 1996), hysteretic biviscous models (Wereley et al., 1998), and mechanism-based models (Kamath and Wereley, 1997; Sims et al., 1999). One nonlinear phenomenon, shear thinning, refers to the reduction in apparent viscosity at high shear rates (Jolly et al., 1999) and has traditionally been modeled with power-law or exponential functions (Wolff-Jesse and Fees, 1998; Wang and Gordaninejad, 1999). These models are complex, and a less complex alternative is to extend the widely-accepted Bingham plastic model. The Bingham plastic model has been successfully used in previous studies to model field dependent rheological fluids (Block and Kelly, 1988; Kamath et al., 1996). This model considers a fluid with a dynamic yield stress, beyond which a linear plastic viscosity is observed. When applied to flow between two parallel plates, the Bingham plastic model predicts a region of fluid that does not shear, having not reached the dynamic yield stress. Approaching the walls, the fluid shear rate increases as the shear stress increases. For high rod velocity and small gap size, this shear rate can reach values known to cause shear thinning (Jolly et al., 1999). The Bingham plastic model predicts a constant plastic viscosity for all shear rates, but this assumption can be inaccurate at high shear rates. This paper proposes a modified Bingham plastic model to account for shear thinning. Rather than fit an exponential curve to the postyield viscosity, the Bingham biplastic approach considers biplastic postyield beha- vior. This approach, while clearly a simplification, may be accurate enough to model MR fluid in most situations. Furthermore, the resulting model is simple enough to readily compare to the Bingham plastic case. For the new model, two parameters are added to the Bingham plastic model. Shear thinning is assumed to *Author to whom correspondence should be addressed. JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol. 00—November 2002 1 1045-389X/02/00 0001–10 $10.00/0 DOI: 10.1106/104538902030906 ß 2002 Sage Publications + [6.11.2002–3:43pm] [1–10] [Page No. 1] FIRST PROOFS i:/Sage/Jim/JIM-30906.3d (JIM) Paper: JIM-30906 Keyword