Free vibration and stability analysis of a multi-span pipe conveying fluid using exact and variational iteration methods combined with transfer matrix method

El-Sayed, T.A.; El-Mongy, Heba H.

doi:10.1016/j.apm.2019.02.006

Cited by 53 publications

(14 citation statements)

References 53 publications

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“…Here, we shall provide our contribution in providing the exact solution to equation (17) with boundary conditions (8). Integrating (17) twice with respect to x, we obtain that the general solution to equation (17) is…”

Section: B Steady State Modelmentioning

confidence: 99%

“…Rahamathunissa and Rajendran [10] used variational iteration method to obtain the exact solution to equation (17) with initial conditions (13), and obtained that it is…”

Section: B Steady State Modelmentioning

confidence: 99%

“…The unsaturated and saturated steady state solutions to the initial value problem have been obtained by Rahamathunissa and Rajendran [10] using a variational iteration method. The variational iteration method was due to He [12,13,14] and it has been successfully used to solve various problems [15,16,17,18,19,20,21,22,23,24] including the mathematical chemistry areas [25,26,27,28,29,30].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some Numerical and Analytical Solutions to an Enzyme-Substrate Reaction-Diffusion Problem

Mungkasi

2020

2020 3rd International Seminar on Research of Information Technology and Intelligent Systems (ISRITI)

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Section: B Steady State Modelmentioning

confidence: 99%

“…Rahamathunissa and Rajendran [10] used variational iteration method to obtain the exact solution to equation (17) with initial conditions (13), and obtained that it is…”

Section: B Steady State Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Some Numerical and Analytical Solutions to an Enzyme-Substrate Reaction-Diffusion Problem

Mungkasi

2020

2020 3rd International Seminar on Research of Information Technology and Intelligent Systems (ISRITI)

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“…An improved MOC approach was proposed by Johnston [15] to investigate the fluid transient characteristics. For the frequency domain solution, the transfer matrix method which is abbreviated as TMM was used to investigate FSI problems of pipelines [16][17][18]. Based on the finite element method which is abbreviated as FEM, Sreejith et al [19] investigated the vibration behavior of nuclear pipeline with a sudden valve closure.…”

Section: Introductionmentioning

confidence: 99%

Experimental and Numerical Vibration Analysis of Hydraulic Pipeline System under Multiexcitations

Gao

Zhang

et al. 2020

Shock and Vibration

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Pipeline systems in aircraft are subjected to both hydraulic pump pressure fluctuations and base excitation from the engine. This can cause fatigue failures due to excessive vibrations. Therefore, it is essential to investigate the vibration behavior of the pipeline system under multiexcitations. In this paper, experiments have been conducted to describe the hydraulic pipeline systems, in which fluid pressure excitation in pipeline is driven by the throttle valve, and the base excitation is produced by the shaker driven by a vibration controller. An improved model which includes fluid motion and base excitation is proposed. A numerical MOC-FEM approach which combined the coupling method of characteristics (MOC) and finite element method (FEM) is proposed to solve the equations. The results show that the current MOC-FEM method could predict the vibration characteristics of the pipeline with sufficient accuracy. Moreover, the pipeline under multiexcitations could produce an interesting beat phenomenon, and this dangerous phenomenon is investigated for its consequences from engineering point of view.

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“…In addition to numerical methods, variant of analytical methods, exemplarily, variational iteration method (VIM) (He, 1999), differential transformation method (DTM) (Hussin et al, 2016), homotopy perturbation method (HPM) (He, 2003), and Adomian decomposition method (ADM) (Adomian, 1988), have been utilized to determine the approximate solutions of the ODE. Each of these methods has its limitations, albeit it gains prominence in solving the modeling problems in various fields (Das & Kundu, 2019;El-Sayed & El-Mongy, 2019;Turkyilmazoglu, 2018).…”

Section: Introductionmentioning

confidence: 99%

On the Formulation of Metaheuristic Algorithm-Based Approximation Approach for Nonlinear Ordinary Differential Equations with Application to Heat Exchanger Problem

Low

Ong

2020

JST

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The problems that arise in multitudinous fields often involve solving complex nonlinear ordinary differential equations (ODE), and it remains challenging since the actual solutions to these problems are hard to obtain. In this regard, the solution strategy with the formulation of Fourier series expansion, calculus of variation and metaheuristic algorithm, was introduced to determine the approximate solution of the nonlinear ODE. The nonlinear ODE was formulated as an optimization problem, specifically, the moth-flame optimization (MFO) algorithm and flower pollination algorithm (FPA) were utilized to find the coefficients of the Fourier series. This paper aimed to determine the feasibility of the proposed method to solve the ODEs with different characteristics and compare the obtained results with other optimization algorithms. Moreover, the suitable number of terms (NT) of Fourier series were determined for different test problems for MFO and FPA. The quantitative analysis in terms of the generational distance (GD) metric demonstrated that the approximate solutions were reasonably accurate, with the low GD within the range of 1E-03 to 1E-05 for all test problems. The comparative analysis showed that the approximate performances of MFO and FPA were superior to or comparable with the genetic algorithm, particle swarm optimization and water cycle algorithm.

show abstract

Free vibration and stability analysis of a multi-span pipe conveying fluid using exact and variational iteration methods combined with transfer matrix method

Cited by 53 publications

References 53 publications

Some Numerical and Analytical Solutions to an Enzyme-Substrate Reaction-Diffusion Problem

Some Numerical and Analytical Solutions to an Enzyme-Substrate Reaction-Diffusion Problem

Experimental and Numerical Vibration Analysis of Hydraulic Pipeline System under Multiexcitations

On the Formulation of Metaheuristic Algorithm-Based Approximation Approach for Nonlinear Ordinary Differential Equations with Application to Heat Exchanger Problem

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