this article studied static deflection, natural frequency and nonlinear vibration of a clamped-clamped microbeam under discontinues electrostatic actuation. the electrostatic actuation was induced by applying ac-dc voltage between the microbeam and electrode plate. in contrast to previous works, it was assumed that length of the electrode plate was smaller than that of the microbeam. in additio...

in this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. the homotopy analysis method (ham) is used for solving this equation. several examples are given to reconfirm the efficiency of these algorithms. the results of applying this procedure...

in this paper, nonlinear klein-gordon equation with quadratic term is solved by means of an analytic technique, namely the homotopy analysis method (ham).comparisons are made between the adomian decomposition method (adm), the exact solution and homotopy analysis method. the results reveal that the proposed method is very effective and simple.

It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations which are usually derived by the reductive perturbation theory are shown to be naturally derived as the equations describing the envelopes of the local solution...

We consider a system of differential equations possessing a family of T -periodic solutions and subjected to a T -periodic Lipschitz small perturbation. We prove the existence and uniqueness of a T -periodic solution of the perturbed system by means of a Lipschitz generalization of the Lyapunov–Schmidt reduction method. When the perturbation is continuously differentiable our result coincides w...

In this paper, a new analytical approach has been presented for solving strongly nonlinear oscillator problems. Iteration perturbation method leads us to high accurate solution. Two different high nonlinear examples are also presented to show the application and accuracy of the presented method. The results are compared with analytical methods and with the numerical solution using Runge-Kutta m...

Hamiltonian system LetA ⊆ R be an open set andH :A×R×R → R be a smooth function (A×R is called the phase space). Consider the system of ordinary differential equations q̇k = ∂H(q, p, t)/∂pk, ṗk = −∂H(q, p, t)/∂qk, for k = 1, . . . , d. The equations are called Hamilton equations, and H is called a Hamiltonian function. A dynamical system described by Hamilton equations is called a Hamiltonian sy...

In this paper, Elzaki Homotopy Perturbation Method is employed for solving linear and nonlinear differential equations with a variable coffecient. This method is a combination of Elzaki transform and Homotopy Perturbation Method. The aim of using Elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as Homotopy Perturbat...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...

In this work, thermo – elastic analysis for functionally graded thick – walled cylinder with temperature - dependent material properties at steady condition is carried out. The length of cylinder is infinite and loading is consist of internal hydrostatic pressure and temperature gradient. All of physical and mechanical properties expect the Poisson's ratio are considered as multiplied an expone...