A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation

The aim of this paper is to apply OHAM to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation, thermal relaxation times, and magnetic field. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. This optimal approach has a general meaning and can be used to get fast convergent series solutions of the different type of nonlinear fractional differential equation. The displacement and temperature are calculated for the models with the variations of the magnetic field, relaxation times, and rotation. The results obtained are displayed graphically to show the influences of the new parameters.