ibrabbas7

Prof. Dr. Ibrahim A. Abbas

Professor - Department of Mathematics

Faculty of science

Address: Sohag University, Egypt.

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Publications Which contain the keyword: energy balance method

A Modified Energy Balance Method to Obtain Higher-order Approximations to the Oscillators with Cubic and Harmonic Restoring Force

2019-10-21 12:49:50 Keywords Homotopy Perturbation Method, Iterative procedure, energy balance method, Nonlinear algebraic equations, Strongly nonlinear oscillator, Analytical technique,
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 ... Read more

SOLUTIONS OF THE DUFFING-HARMONIC OSCILLATOR BY HE’S ENERGY BALANCE METHOD

2018-10-24 22:35:25 Keywords energy balance method, nonlinear oscillator, Duffing-harmonic oscillator, Periodic Solutions,
SOLUTIONS OF THE DUFFING-HARMONIC OSCILLATOR BY HE’S ENERGY BALANCE METHOD
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. Read more

Analytical and Approximate Solutions to the Fee Vibration of Strongly Nonlinear Oscillators

2018-10-24 23:04:00 Keywords periodic solution, Nonlinear oscillators, energy balance method, Variational Iteration Method,
Analytical and Approximate Solutions to the Fee Vibration of Strongly Nonlinear Oscillators
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 ... Read more

Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

2018-10-25 07:54:07 Keywords 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 ... Read more

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