Application of optimal homotopy asymptotic method to nonlinear Bingham fluid dampers

TL;DR

This paper demonstrates how the Optimal Homotopy Asymptotic Method (OHAM) can efficiently solve nonlinear differential equations modeling Bingham fluid dampers, providing rapid convergence without small parameters.

Contribution

It introduces the application of OHAM to nonlinear Bingham fluid damper equations, offering a new analytical approach with fast convergence and minimal computational steps.

Findings

OHAM achieves rapid convergence in solving Bingham damper equations.

The method does not rely on small parameters, simplifying analysis.

Results indicate high efficiency and accuracy of the approach.

Abstract

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.