جمال محمد إسماعيل حسان

استاذ مساعد - استاذ مساعد بقسم الرياضيات - كلية العلوم - جامعة سوهاج

كلية العلوم

العنوان: قسم الرياضيات - كلية العلوم - جامعة سوهاج


A Modified Energy Balance Method to Obtain Higher-order Approximations to the Oscillators with Cubic and Harmonic Restoring Force
This article analyzes a strongly nonlinear oscillator with cubic and harmonic restoring force and proposes an efficient analytical technique based on the modified energy balance method (MEBM). The proposed method incorporates higher-order approximations. After applying the proposed MEBM, a set of complicated higher-order nonlinear algebraic equations are obtained. Higher-order nonlinear algebraic equations are cumbersome to investigate especially in the case ... إقراء المزيد

An analytical solution for fractional oscillator in a resisting medium
In this paper, an analytical exact solution for the fractional differential equation of the oscillator in a resisting medium was obtained successfully via the natural transform method. The fractional derivatives were described in the Caputo sense. The results illustrated the power, efficiency, simplicity, and reliability of the proposed method إقراء المزيد

An Accurate Analytical Solution to Strongly Nonlinear Differential Equations
Abstract: The study presents an alternative analytical method called Newton Harmonic Balance Method (NHBM) to provide an analytical solution for two nonlinear differential equations that appear in specific dynamics. This method is based on combining Newton’s method and the harmonic balance method. Because the periodic solution is analytically proved, the relation between the natural frequency and the amplitude is obtained ... إقراء المزيد

Analytical approximations to nonlinear oscillation of nanoelectro-mechanical resonators
Abstract. We introduce a new analytical-approximate method based on the global residue harmonic balance method (GRHBM) to study the oscillation of nonlinear nanoelectromechanical resonators. The proposed method is efficiently implemented and evaluated numerically. An illustrative example demonstrates the validity and applicability of the method, further discussed in detail. A highly remarkable agreement found between the approximated solution obtained with the ... إقراء المزيد

Higher-order approximate periodic solution for the oscillator with strong nonlinearity of polynomial type
In this paper the harmonic balance method (HBM) is adopted for solving a special group of oscillators with strong nonlinear damping and elastic forces. The nonlinearity is of polynomial type. The motion is described with a strong nonlinear differential equation, whose approximate solution is assumed as a suitable sum of trigonometric functions. To find the most convenient combination of trigonometric ... إقراء المزيد

2017 | الكلمات المفتاحية Strongly nonlinear oscillator, analytical solution,
An analytical coupled homotopy-variational approach for solving strongly nonlinear differential equation
In the present paper, a novel technique combining the homotopy concept with variational formula has been presented to find accurate analytical solution for nonlinear differential equation with inertia and static non-linearity. The obtained results are compared with other analytical and exact solutions to confirm the excellent accuracy and correctness of the approximate analytical technique. The results of the present paper ... إقراء المزيد

2016 | الكلمات المفتاحية Duffing oscillators, perturbation technique,
Analytical solution of strongly nonlinear Duffing oscillators
In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter is defined such that the value of is always small regardless of the magnitude of the original parameter . Therefore, the strongly nonlinear Duffing oscillators with large parameter e are transformed into a small parameter system with respect to a. ... إقراء المزيد

An Analytical Technique for Solving Nonlinear Oscillators of the Motion of a Rigid Rod Rocking Bock and Tapered Beams
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 method in different ... إقراء المزيد

2016 | الكلمات المفتاحية energy balance method, Duffing harmonic oscillator, Periodic solutions.,
Periodic Solutions of the Duffing Harmonic Oscillator  by He's Energy Balance Method
Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solutions using Runge-Kutta method. The ... إقراء المزيد

Analytical Solutions of Strongly Non-linear Problems by the Iteration Perturbation Method
This paper applies modified He's iteration perturbation method to study periodic solutions of strongly nonlinear oscillators. Some examples are given to illustrate the effectiveness and convenience of the method. The results are compared with the numerical solution and the comparison showed a proper accuracy of this method. إقراء المزيد