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2014 1

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Algebraic Method (AGM) 1

Angular Frequency 1

Duffing 1

He’s energy balance method 1

Rayleigh 1

Vanderpol 1

duffing equation 1

mathematical pendulum 1

min-max method 1

nonlinear oscillation 1

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Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

M. R. AKBARI,D. D. GANJI,A. MAJIDIAN,A. R. AHMADI

Frontiers of Mechanical Engineering 2014, Volume 9, Issue 2, Pages 177-190 doi: 10.1007/s11465-014-0288-8

Abstract: complicated nonlinear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing

Keywords： Algebraic Method (AGM) Angular Frequency Vanderpol Rayleigh Duffing

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Numerical analysis of strongly nonlinear oscillation systems using He’s max-min method

H. BABAZADEH, G. DOMAIRRY, A. BARARI, R. AZAMI, A. G. DAVODI

Frontiers of Mechanical Engineering 2011, Volume 6, Issue 4, Pages 435-441 doi: 10.1007/s11465-011-0243-x

Abstract:

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.

Keywords： min-max method nonlinear oscillation duffing equation mathematical pendulum He’s energy balance method