Analytical solution to nonlinear oscillation system of the motion of a rigid rod rocking back using max–min approach

Ganji, S. S.; Ganji, D. D.; Davodi, A. G.; Karimpour, S.

doi:10.1016/j.apm.2009.12.002

Cited by 36 publications

(21 citation statements)

References 13 publications

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“…This method has been used as a reliable benchmark for evaluating the novel analytical approaches to nonlinear oscillation system [36][37][38]. In following Mathematical formulation and geometry of problem are presented in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Study on motion of rigid rod on a circular surface using MHPM

Ghasemi

Zolfagharian

Ganji

2014

Propulsion and Power Research

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In this paper motion of rigid rod on a circular surface is studied analytically. A new analytical method called modified homotopy perturbation method (MHPM) is applied for solving this problem in different initial conditions to show capability of this method. The governing equation for motion of a rigid rod on the circular surface without slipping have been solved using MHPM. The efficacy of MHPM for handling nonlinear oscillation systems with various small and large oscillation amplitudes are presented in comparison with numerical benchmarks. Outcomes reveal that MHPM has an excellent agreement with numerical solution. The results show that by decreasing the oscillation amplitude, the velocity of rigid rod decreases and for A¼π/3 the velocity profile is maximum.

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Section: Introductionmentioning

confidence: 99%

Study on motion of rigid rod on a circular surface using MHPM

Ghasemi

Zolfagharian

Ganji

2014

Propulsion and Power Research

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“…When an oscillatory system includes damping, there is a nonconservative system and, in contrast to the conservative one [5{8], the amplitude of oscillations decreases over time. Most of analytical approaches such as maxmin approach [9,10], Hamiltonian approach [11], and modi ed variational technique [12] are unable to handle non-conservative systems.…”

Section: Introductionmentioning

confidence: 99%

Application of AG method and its improvement to nonlinear damped oscillators

Mohammadian

Shariati

2018

Scientia Iranica

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In this paper, a new and innovative semi-analytical technique, namely Akbari-Ganji's Method (AGM), is employed for solving three nonlinear damped oscillatory systems. Applying this method to nonlinear problems is very simple because, in the solving process of only a trial solution, the main di erential equation and its derivatives are required. The analytical solutions obtained by AGM are utilized to study the impact of amplitude on nonlinear frequency and damping ratio. It is found that AGM produces acceptable results for the problems considered in this paper. Moreover, in order to obtain a more accurate solution, instead of using a trial solution with higher-order terms that may result in complicated and time-consuming mathematical calculations, the solution obtained by AGM is improved via Variational Iteration Method (VIM). The usefulness and e ectiveness of the approach is demonstrated through the comparison of the obtained results and those achieved by the numerical method. Hence, AGM can be applied to nonlinear problems consisting of signi cant nonlinear damping terms and, if necessary, can be easily improved.

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“…The Max-Min approach is developed from the idea of ancient Chinese math and owns the property of convenient application, less calculation and high accuracy, and so forth. Among current researches about He's Max-Min approach and its applications [4][5][6][7][8][9][10], few involve coupled nonlinear problems such in packaging engineering, especially the higher-dimensional coupled nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

He’s Max-Min Approach for Coupled Cubic Nonlinear Equations Arising in Packaging System

Wang

2013

Mathematical Problems in Engineering

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He’s inequalities and the Max-Min approach are briefly introduced, and their application to a coupled cubic nonlinear packaging system is elucidated. The approximate solution is obtained and compared with the numerical solution solved by the Runge-Kutta algorithm yielded by computer simulation. The result shows a great high accuracy of this method. The research extends the application of He’s Max-Min approach for coupled nonlinear equations and provides a novel method to solve some essential problems in packaging engineering.

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Analytical solution to nonlinear oscillation system of the motion of a rigid rod rocking back using max–min approach

Cited by 36 publications

References 13 publications

Study on motion of rigid rod on a circular surface using MHPM

Study on motion of rigid rod on a circular surface using MHPM

Application of AG method and its improvement to nonlinear damped oscillators

He’s Max-Min Approach for Coupled Cubic Nonlinear Equations Arising in Packaging System

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