Browsing by Author "Senturk, Erman"

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Analysis of the motion of a rigid rod on a circular surface using interpolated variational iteration method
(YILDIZ TECHNICAL UNIV, 2022) Coskun, Safa Bozkurt; Senturk, Erman; Atay, Mehmet Tarik; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü; Atay, Mehmet Tarik
In this paper, interpolated variational iteration method (IVIM) is applied to investigate the vibration period and steady-state response for the motion of rigid rod rocking back and forth on a circular surface without slipping. The problem can be considered as a strongly nonlinear oscillator. In this solution procedure, analytical variational iteration technique is utilized by evaluating the integrals numerically. The approximate analytical results produced by the presented method are compared with the other existing solutions available in the literature. The advantage of using numerical evaluation of integrals, the method becomes fast convergent and a highly accurate solution can be obtained within seconds. The authors believe that the presented technique has potentially wide application in the other nonlinear oscillation problems.
Interpolated variational iteration method for solving the jamming transition problem
(ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS, 2019) Coskun, Safa Bozkurt; Atay, Mehmet Tarik; Senturk, Erman; 0000-0002-0833-7113; AGÜ, Mühendislik Fakültesi, Makine Mühendisliği Bölümü
The purpose of this study is to present an analytical based numerical solution for Jamming Transition Problem (JTP) using Interpolated Variational Iteration Method (IVIM). The method eliminates the difficulties on analytical integration of expressions in analytical variational iteration technique and provides numerical results with analytical accuracy. JTP may be transformed into a nonlinear non-conservative oscillator by Lorenz system in which jamming transition is presented as spontaneous deviations of headway and velocity caused by the acceleration/breaking rate to be higher than the critical value. The resulting governing equation of JTP has no exact solution due to existing nonlinearities in the equation. The problem was previously attempted to be solved semi-analytically via analytical approximation methods including analytical variational iteration technique. The results of this study show that IVIM solutions agree very well with the numerical solution provided by the mathematical software. IVIM with two different formulation according to governing equation is introduced. Required order of the solution and number of time steps for a good agreement is determined according to the analyses performed using IVIM. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Solution of jamming transition problem using adomian decomposition method
(EMERALD GROUP PUBLISHING LTD, HOWARD HOUSE, WAGON LANE, BINGLEY BD16 1WA, W YORKSHIRE, ENGLAND, 2018) Senturk, Erman; Coskun, Safa Bozkurt; Atay, Mehmet Tarik; 0000-0002-0833-7113; AGÜ, Mühendislik Fakültesi, Makine Mühendisliği Bölümü
Purpose The purpose of the study is to obtain an analytical approximate solution for jamming transition problem (JTP) using Adomian decomposition method (ADM). Design/methodology/approach In this study, the jamming transition is presented as a result of spontaneous deviations of headway and velocity that is caused by the acceleration/breaking rate to be higher than the critical value. Dissipative dynamics of traffic flow can be represented within the framework of the Lorenz scheme based on the car-following model in the one-lane highway. Through this paper, an analytical approximation for the solution is calculated via ADM that leads to a solution for headway deviation as a function of time. Findings A highly nonlinear differential equation having no exact solution due to JTP is considered and headway deviation is obtained implementing a number of different initial conditions. The results are discussed and compared with the available data in the literature and numerical solutions obtained from a built-in numerical function of the mathematical software used in the study. The advantage of using ADM for the problem is presented in the study and discussed on the basis of the results produced by the applied method. Originality/value This is the first study to apply ADM to JTP.