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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
Numerical analysis of strongly nonlinear oscillation systems using He’s max-min method
H. BABAZADEH, G. DOMAIRRY, A. BARARI, R. AZAMI, A. G. DAVODI
《机械工程前沿（英文）》 2011年 第6卷 第4期 页码 435-441 doi: 10.1007/s11465-011-0243-x
Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method for presenting an accurate approximate analytical solution to strong nonlinear oscillators. It can solve many linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term. It is also quite convenient due to the reduction in the size of calculations. The algorithm suggests a promising approach and is systematically illustrated step by step.
关键词： min-max method nonlinear oscillation duffing equation mathematical pendulum He’s energy balance method
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