Application of AFF and HPM to the systems of strongly nonlinear oscillation

S.S. Ganji,D.D. Ganji,M.G. Sfahani,S. Karimpour 한국물리학회 2010 Current Applied Physics Vol.10 No.5

This study is concerned with two well-known systems of nonlinear oscillators. One of them is a system consists of a mass grounded two springs which one of those springs is linear and the other is nonlinear, and the other one is dealt with nonlinear large amplitude free vibrations of a slender cantilever beam with a rotationally flexible root and carrying a lumped mass at an intermediate position along its span. The main objective was to obtain highly accurate analytical solutions for free vibration of conservative oscillators with inertia and static type cubic nonlinearities. Two methods are studied to analyze the dynamic system behavior. One method makes use of a set of Amplitude–Frequency Formulation (AFF) and the other method applies Homotopy Perturbation Method (HPM). Taking advantage of some simple mathematical operations on these methods, we can obtain their natural frequencies. The computed results agree with those analytical and numerical results given in the literatures. The results indicate that the present analysis is accurate, and provide us a unified and systematic procedure which is simple and more straightforward than the other similar methods.

Application of the energy balance method to nonlinear vibrating equations

I. Mehdipour,D.D. Ganji,M. Mozaffari 한국물리학회 2010 Current Applied Physics Vol.10 No.1

In this paper, He’s energy balance method is applied to nonlinear vibrations and oscillations. The method is applied to four nonlinear differential equations. It has indicated that by utilizing He’s energy balance method (HEBM), just one iteration leads us to high accuracy of solutions. It has illustrated that the energy balance methodology is very effective and convenient and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance method, only one iteration leads to high accuracy of the solutions. The results reveal that the energy balance method is very effective and simple. It is predicted that the energy balance method can be found wide application in engineering problems, as indicated in following examples.

Nonlinear vibration and rippling instability for embedded carbon nanotubes

Payam Soltani,D. D. Ganji,I. Mehdipour,A. Farshidianfar 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.4

Based on the rippling deformations, a nonlinear continuum elastic model is developed to analyze the transverse vibration of singlewalled carbon nanotubes (SWCNTs) embedded on a Winkler elastic foundation. The nonlinear natural frequency has been derived analytically for typical boundary conditions using the perturbation method of multi-scales. The results indicate that the nonlinear resonant frequency due to the rippling is related to the stiffness of the foundation, the boundary conditions, the excitation load-to-damping ratio,and the diameter-to-length ratio. Moreover, the rippling instability of carbon nanotubes, as a structural instability, is introduced and the influences of several effective parameters on this kind of instability are widely discussed.

Nonlinear fluctuation, frequency and stability analyses in free vibration of circular sector oscillation systems

M. Shaban,D.D. Ganji,M.M. Alipour 한국물리학회 2010 Current Applied Physics Vol.10 No.5

In the present paper, the modified homotopy perturbation method (MHPM) is employed to investigate about both nonlinear swinging oscillation and the stability of circular sector oscillation systems. The sensitivity study performed for frequency analysis of the mentioned oscillatory circular sector body shows that frequency of nonlinear oscillation depends on some specific parameters and can be optimized. Furthermore onset of the instability is dependent to angle α and initial amplitude. Comparisons made among the results of the present closed-form analytical solution and the traditional numerical iterative time integration solution confirms the accuracy and efficiency of the presented analytical solution. In contrast to the available numerical methods, the present analytical method is free from the numerical damping and the time integration accumulated errors. Moreover, in comparison with the traditional multistep numerical iterative time integration methods, a much less computational time is required for the present analytical method. Responses of the dynamical systems to some extent are affected by the natural frequencies. Results reveal that for nonlinear systems, the natural frequency is remarkably affected by the initial conditions.

Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire

N. Jamshidi,D.D. Ganji 한국물리학회 2010 Current Applied Physics Vol.10 No.2

This letter applies energy balance method and variational iteration method to a nonlinear oscillation of a mass attached to a stretched wire. Comparison of the period of oscillation and obtained solutions with the exact one shows that both methods are very effective and convenient and quite accurate to nonlinear engineering problems.

Slope variation effect on large deflection of compliant beam using analytical approach

Khavaji, A.,Ganji, D.D.,Roshan, N.,Moheimani, R.,Hatami, M.,Hasanpour, A. Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.44 No.3

In this study the investigation of large deflections subject in compliant mechanisms is presented using homotopy perturbation method (HPM). The main purpose is to propose a convenient method of solution for the large deflection problem in compliant mechanisms in order to overcome the difficulty and complexity of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, a cantilever beam of linear elastic material under horizontal, vertical and bending moment end point load is considered. The results show that the applied method is very accurate and capable for cantilever beams and can be used for a large category of practical problems for the aim of optimization. Also the consequence of effective parameters on the large deflection is analyzed and presented.

Slope variation effect on large deflection of compliant beam using analytical approach

A. Khavaji,D.D. Ganji,N. Roshan,R. Moheimani,M. Hatami,A. Hasanpour 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.44 No.3

In this study the investigation of large deflections subject in compliant mechanisms is presented using homotopy perturbation method (HPM). The main purpose is to propose a convenient method of solution for the large deflection problem in compliant mechanisms in order to overcome the difficulty and complexity of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, a cantilever beam of linear elastic material under horizontal, vertical and bending moment end point load is considered. The results show that the applied method is very accurate and capable for cantilever beams and can be used for a large category of practical problems for the aim of optimization. Also the consequence of effective parameters on the large deflection is analyzed and presented.

First principles study of the I–V characteristics of the alkane-thiols nano-molecular wires

H. Aghaie,M.R. Gholami,M.D. Ganji,M.M. Taghavi 한국물리학회 2009 Current Applied Physics Vol.9 No.3

We report a density functional non-equilibrium Green’s function study of electrical transport in a single molecular conductor consisting of an ethane-dithiolate (C2H4S2) molecular wire with two sulfur end groups bonded to the Au(111) electrodes. We show that the current was increased by increasing the external voltage biases. The projected density of states (PDOS) and transmission coefficients T(E) under various external voltage biases are analyzed, and it suggests that the variation of the coupling between the molecule and the electrodes with external bias leads to the increase of the current. Furthermore, the investigation of the transport properties of the pentane- dithiolate (C5H10S2) molecular wire shows that the pentane-dithiolate molecular wire has a lower conductivity than the ethanedithiolate wire. We report a density functional non-equilibrium Green’s function study of electrical transport in a single molecular conductor consisting of an ethane-dithiolate (C2H4S2) molecular wire with two sulfur end groups bonded to the Au(111) electrodes. We show that the current was increased by increasing the external voltage biases. The projected density of states (PDOS) and transmission coefficients T(E) under various external voltage biases are analyzed, and it suggests that the variation of the coupling between the molecule and the electrodes with external bias leads to the increase of the current. Furthermore, the investigation of the transport properties of the pentane- dithiolate (C5H10S2) molecular wire shows that the pentane-dithiolate molecular wire has a lower conductivity than the ethanedithiolate wire.

Analytical thermal analysis of air-heating solar collectors

S. E. Ghasemi,M. Hatami,D. D. Ganji 대한기계학회 2013 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.27 No.11

In this paper, Optimal Homotopy Asymptotic Method (OHAM) and Homotopy perturbation method (HPM) are applied to investigate heat transfer in the air-heating flat-plate solar collectors. Results for different values of active parameters are compared with numerical method (fourth order Runge-Kutta method). The results confirm the notion that the HPM method is more accurate than OHAM and efficient technique for finding exact solutions for differential equations which have great significance in different fields of science and engineering. Effects of air flow rate, width and length of the collector on thermal efficiency are examined. As an important outcome, increasing in the collector’s dimensions (width and length) make a decreasing in thermal efficiency, but increasing in air mass flow rates improve it.

Analysis of modified Van der Pol’s oscillator using He’s parameter-expanding methods

A. Kimiaeifar,A.R. Saidi,A.R. Sohouli,D.D. Ganji 한국물리학회 2010 Current Applied Physics Vol.10 No.1

In this work, a powerful analytical method, called He’s parameter-expanding methods (HPEM) is used to obtain the exact solutions of non-linear modified Van der Pol’s oscillator. The classical Van der Pol equation with delayed feedback and a modified equation where a delayed term provides the damping are considered. It is shown that one term in series expansions is sufficient to obtain a highly accurate solution,which is valid for the whole solution domain. Comparison of the obtained solution with those obtained using perturbation method shows that this method is effective and convenient to solve this problem. This method introduces a capable tool to solve this kind of non-linear problems.