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M. R. AKBARI,D. D. GANJI,M. NIMAFAR,A. R. AHMADI
《机械工程前沿（英文）》 2014年 第9卷 第4期 页码 390-401 doi: 10.1007/s11465-014-0313-y
In this paper, we aim to promote the capability of solving two complicated nonlinear differential equations: 1) Static analysis of the structure with variable cross section areas and materials with slope-deflection method; 2) the problem of one dimensional heat transfer with a logarithmic various surface A(x) and a logarithmic various heat generation G(x) with a simple and innovative approach entitled “Akbari-Ganji’s method” (AGM). Comparisons are made between AGM and numerical method, the results of which reveal that this method is very effective and simple and can be applied for other nonlinear problems. It is significant that there are some valuable advantages in this method and also most of the differential equations sets can be answered in this manner while in other methods there is no guarantee to obtain the good results up to now. Brief excellences of this method compared to other approaches are as follows: 1) Differential equations can be solved directly by this method; 2) without any dimensionless procedure, equation(s) can be solved; 3) it is not necessary to convert variables into new ones. According to the aforementioned assertions which are proved in this case study, the process of solving nonlinear equation(s) is very easy and convenient in comparison to other methods.
关键词： AGM extended surface heat transfer slope-deflection method
Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM
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《机械工程前沿（英文）》 2014年 第9卷 第2期 页码 177-190 doi: 10.1007/s11465-014-0288-8
In the present paper, three complicated nonlinear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method (AGM). Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method (Runge-Kutte 4th). Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems.
关键词： Algebraic Method (AGM) Angular Frequency Vanderpol Rayleigh Duffing
M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI
《机械工程前沿（英文）》 2014年 第9卷 第1期 页码 58-70 doi: 10.1007/s11465-014-0289-7
In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.
关键词： Algebraic Method (AGM) tower crane oscillating system angular frequency
M. R. AKBARI,M. NIMAFAR,D. D. GANJI,M. M. AKBARZADE
《机械工程前沿（英文）》 2014年 第9卷 第4期 页码 402-408 doi: 10.1007/s11465-014-0316-8
The kinematic assumptions upon which the Euler-Bernoulli beam theory is founded allow it to be extended to more advanced analysis. Simple superposition allows for three-dimensional transverse loading. Using alternative constitutive equations can allow for viscoelastic or plastic beam deformation. Euler-Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinear beam deflection. In this study, solving the nonlinear differential equation governing the calculation of the large rotation deviation of the beam (or column) has been discussed. Previously to calculate the rotational deviation of the beam, the assumption is made that the angular deviation of the beam is small. By considering the small slope in the linearization of the governing differential equation, the solving is easy. The result of this simplification in some cases will lead to an excessive error. In this paper nonlinear differential equations governing on this system are solved analytically by Akbari-Ganji’s method (AGM). Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration solving. The solution of the problem can be obtained very simply and easily. Furthermore, to enhance the accuracy of the results, the Taylor expansion is not needed in most cases via AGM manner. Also, comparisons are made between AGM and numerical method (Runge-Kutta 4th). The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems.
关键词： AGM critical load of columns large deformations of beam nonlinear differential equation
标题 作者 时间 类型 操作
solution of nonlinear equations at displacement of structure and heat transfer extended surface by new AGM
M. R. AKBARI,D. D. GANJI,M. NIMAFAR,A. R. AHMADI
期刊论文
Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method
M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI
期刊论文
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