جمال محمد إسماعيل حسان

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

كلية العلوم

العنوان: قسم الرياضيات - كلية العلوم - جامعة سوهاج

7

إعجاب

#### المنشورات و المؤلفات التي تحتوي علي الكلمة المفتاحية: energy balance method

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 ...

2018-10-24 22:35:25 الكلمات المفتاحية energy balance method, nonlinear oscillator, Duffing-harmonic oscillator, Periodic Solutions,
ABSTRACT: In this paper, He’s energy balance method is applied to nonlinear oscillators. The obtained results are valid for the whole solution domain with high accuracy. Comparison is made with the solutions obtained by using He’s frequency-amplitude formulation and Runge-Kutta method to show the efficiency of the energy balance method.

2018-10-24 23:04:00 الكلمات المفتاحية periodic solution, Nonlinear oscillators, energy balance method, Variational Iteration Method,
In this paper, we implement a new approach coupled with the iteration method. This procedure is obtained by combining He’s frequency-amplitude formulation and He’s energy balance method into a new iteration procedure such that excellent approximate analytical solutions, valid for small as well as large values of amplitude, can be determined for nonlinear oscillators. This study has clarified the motion ...

2018-10-25 07:54:07 الكلمات المفتاحية energy balance method, Duffing harmonic oscillator, Periodic solutions.,
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 ...

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