The paper is concern to the approximate analytical solution of K(2,2) using multistage homotopy asymptotic method which are used in modern physics and engineering. suggested algorithm an accurate, effective, simple to-utilize semi-analytic tool for non-linear problems, this manner current investigation highlights efficiency accuracy PDE large time span. Numerical comparison with variational ite...

this paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using homotopy perturbation method with an auxiliary term (hpmat). the governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the pro...

the present research attempts to explain dynamic pull-in instability of functionally graded micro-cantilevers actuated by step dc voltage while the fringing-field effect is taken into account in the vibrational equation of motion. by employing modern asymptotic approach namely homotopy perturbation method with an auxiliary term, high-order frequency-amplitude relation is obtained, then the infl...

An incompressible MHD flow of two-dimensional upper-convected Maxwell fluid over a porous stretching plate with suction is studied. The nonlinear differential equation is solved approximately by means of the Optimal Homotopy Asymptotic Method (OHAM). Multiple solutions are given, showing a very good agreement between the analytical and numerical solutions. This procedure is very efficient in pr...