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: Nonlinear oscillators

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 ...

2018-10-24 22:41:59 الكلمات المفتاحية Nonlinear oscillators, He's amplitude-frequency formu, periodic solution,
In this paper, He's amplitude-frequency formulation is used to obtain a periodic solution of a nonlinear oscillator. We illustrate that He's amplitude-frequency formulation is very effective and convenient and does not require linearization or small perturbation. The obtained results are valid for the whole solution domain with high accuracy.

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 ...

In this study, homotopy perturbation method and parameter expanding method are applied to the motion equations of two nonlinear oscillators. Our results show that both the (HPM) and (PEM) yield the same results for the nonlinear problems. In comparison with the exact solution, the results show that these methods are very convenient for solving nonlinear equations and also can be ...

2018-10-24 23:14:36 الكلمات المفتاحية Iteration perturbation method, Nonlinear oscillators, Duffing oscillator, Van der Pol oscillator,
In this paper, the iteration perturbation method is applied to solve nonlinear oscillations. Two examples are given to illustrate the effectiveness and convenience of this iteration procedure. Comparison with the numerical solutions is also presented, revealing that this iteration leads to accurate solutions.

2018-10-25 07:34:30 الكلمات المفتاحية Variational Iteration Method, Nonlinear oscillators, periodic solution,
In this paper, a nonlinear free vibration of strongly nonlinear oscillators is studied. To this end, we propose a novel technique using He’s frequency-amplitude formulation and He’s energy balance method called iteration perturbation procedure. A novel technique called iteration perturbation procedure and variational iteration method are presented to obtain the relationship between amplitude and angular frequency. The obtained results are ...

2018-10-25 07:51:01 الكلمات المفتاحية Tapered beams, Motion of a rigid rod rocking, Nonlinear oscillators, periodic solution,
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 ...

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