  Magnetorheological fluids (MR) are stable suspensions of magnetizable
microparticles, characterized by the property to change the rheological
characteristics when subjected to the action of magnetic field. Together with
another class of materials that change their rheological characteristics in the
presence of an electric field, called electrorheological materials are known in
the literature as the smart materials or controlled materials. In the absence
of a magnetic field the particles in MR fluid are dispersed in the base fluid
and its flow through the apertures is behaves as a Newtonian fluid having a
constant shear stress. When the magnetic field is applying a MR fluid behavior
change, and behaves like a Bingham fluid with a variable shear stress. Dynamic
response time is an important characteristic for determining the performance of
MR dampers in practical civil engineering applications. The purpose of this
paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to
solve the nonlinear differential equation of a modified Bingham model with
non-viscous exponential damping. Our procedure does not depend upon small
parameters and provides us with a convenient way to optimally control the
convergence of the approximate solutions. OHAM is very efficient in practice
ensuring a very rapid convergence of the solution after only one iteration and
with a small number of steps.
