An analytical investigation and comparison of oscillating systems with nonlinear behavior using AGM and HPM

Samadi, Hamid; Mohammadi, Nikta Shams; Shamoushaki, Mohammad; Asadi, Zohreh; Ganji, D.D.

doi:10.1016/j.aej.2022.02.036

Cited by 11 publications

(4 citation statements)

References 35 publications

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“…Based on their results, the Akabari-Ganji method (AGM) demonstrated the highest accuracy compared to finite element method, numerical method and differential transform method. Samadi et al (2022) analytically solved problems using AGM and homotopy perturbation method, demonstrating the feasibility and sufficient accuracy of these methods for solving oscillation problems. In the current study, the feasibility of analytical modeling (ARB) to model temperature history in DED is implemented.…”

Section: Introductionmentioning

confidence: 97%

Modeling the effect of processing parameters on temperature history in Directed Energy Deposition: an analytical and finite element approach

Ghasempour-Mouziraji,

Afonso,

Hosseinzadeh

et al. 2023

RPJ

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Purpose The purpose of this paper is to assess the feasibility of analytical models, specifically the radial basis function method, Akbari–Ganji method and Gaussian method, in conjunction with the finite element method. The aim is to examine the impact of processing parameters on temperature history. Design/methodology/approach Through analytical investigation and finite element simulation, this research examines the influence of processing parameters on temperature history. Simufact software with a thermomechanical approach was used for finite element simulation, while radial basis function, Akbari–Ganji and Gaussian methods were used for analytical modeling to solve the heat transfer differential equation. Findings The accuracy of both finite element and analytical methods was validated with about 90%. The findings revealed direct relationships between thermal conductivity (from 100 to 200), laser power (from 400 to 800 W), heat source depth (from 0.35 to 0.75) and power absorption coefficient (from 0.4 to 0.8). Increasing the values of these parameters led to higher temperature history. On the other hand, density (from 7,600 to 8,200), emission coefficient (from 0.5 to 0.7) and convective heat transfer (from 35 to 90) exhibited an inverse relationship with temperature history. Originality/value The application of analytical modeling, particularly the utilization of the Akbari–Ganji, radial basis functions and Gaussian methods, showcases an innovative approach to studying directed energy deposition. This analytical investigation offers an alternative to relying solely on experimental procedures, potentially saving time and resources in the optimization of DED processes.

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Section: Introductionmentioning

confidence: 97%

Modeling the effect of processing parameters on temperature history in Directed Energy Deposition: an analytical and finite element approach

Ghasempour-Mouziraji,

Afonso,

Hosseinzadeh

et al. 2023

RPJ

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“…There are many methods to solve nonlinear problems, such as the Homotopy perturbation method (HPM) [3], which is used to solve attachment oscillations that occur in nanotechnology. The nonlinear oscillation system was studied using the Akbari Ganji method [4]. The energy balance method (EBM) [5] investigated the behavior of CNTnano resonators.…”

Section: Introductionmentioning

confidence: 99%

Solutions of the Nonlinear Evolution Problems and their Applications

Amir

Haider

Rahman

et al. 2023

Acta Mechanica Et Automatica

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In this article, a well-known technique, the variational iterative method with the Laplace transform, is used to solve nonlinear evolution problems of a simple pendulum and mass spring oscillator, which represents the duffing equation. In the variational iteration method (VIM), finding the Lagrange multiplier is an important step, and the variational theory is often used for this purpose. This paper shows how the Laplace transform can be used to find the multiplier in a simpler way. This method gives an easy approach for scientists and engineers who deal with a wide range of nonlinear problems. Duffing equation is solved by different analytic methods, but we tackle this for the first time to solve the duffing equation and the nonlinear oscillator by using the Laplace-based VIM. In the majority of cases, Laplace variational iteration method (LVIM) just needs one iteration to attain high accuracy of the answer for linearization anddiscretization, or intensive computational work is needed. The convergence criteria of this method are efficient as compared with the VIM. Comparing the analytical VIM by Laplace transform with MATLAB’s built-in command Simulink that confirms the method’s suitability for solving nonlinear evolution problems will be helpful. In future, we will be able to find the solution of highly nonlinear oscillators.

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“…Homotopy perturbation method was applied by others 13,14 appropriately. Also, many researchers were applied the harmonic balance method, 15 the energy balance method, 16 He's frequency formulation method, 17,18 the variational iteration method, [19][20][21][22] the homotopy analysis method, 23,24 VIM-Pade technique 25,26 etc.…”

Section: Introductionmentioning

confidence: 99%

A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force

Sharif,

Molla,

Alim

2023

Journal of Low Frequency Noise, Vibration and Active Control

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In this article, a very simple modified form of the harmonic balance method is used to solve a strongly nonlinear oscillator with cubic nonlinearity and harmonic restoring force. Taylor series expansion up to third term is considered for the harmonic restoring force. The first approximate solutions of the present method pleasantly agree with the numerical solution obtained by Runge–Kutta fourth order method. Accuracy and simplicity of the present method solution is established when compared with the other method solutions. The present method can be utilized to other nonlinear oscillators.

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An analytical investigation and comparison of oscillating systems with nonlinear behavior using AGM and HPM

Cited by 11 publications

References 35 publications

Modeling the effect of processing parameters on temperature history in Directed Energy Deposition: an analytical and finite element approach

Modeling the effect of processing parameters on temperature history in Directed Energy Deposition: an analytical and finite element approach

Solutions of the Nonlinear Evolution Problems and their Applications

A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force

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