Browsing by Author "Çevik M."
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Item Natural frequencies of suspension bridges: An artificial neural network approach(Academic Press, 2002) Çevik M.; Özkaya E.; Pakdemirli M.[No abstract available]Item Non-linear vibrations of suspension bridges with external excitation(2005) Çevik M.; Pakdemirli M.Non-linear coupled vertical and torsional vibrations of suspension bridges are investigated. Method of Multiple Scales, a perturbation technique, is applied to the equations to find approximate analytical solutions. The equations are not discretized as usually done, rather the perturbation method is applied directly to the partial differential equations. Free and forced vibrations with damping are investigated in detail. Amplitude and phase modulation equations are obtained. The dependence of non-linear frequency on amplitude is described. Steady-state solutions are analyzed. Frequency-response equation is derived and the jump phenomenon in the frequency-response curves resulting from non-linearity is considered. Effects of initial amplitude and phase values, amplitude of excitation, and damping coefficient on modal amplitudes, are determined. © 2005 Elsevier Ltd. All rights reserved.Item Taylor matrix solution of the mathematical model of the RLC circuits(Association for Scientific Research, 2013) Bahşi M.M.; Çevik M.The RLC circuit is a basic building block of the more complicated electrical circuits and networks. The present study introduces a novel and simple numerical method for the solution this problem in terms of Taylor polynomials in the matrix form. Particular and general solutions of the related differential equation can be determined by this method. The method is illustrated by a numerical application and a quite good agreement is observed between the results of the present method and those of the exact method.Item Solution of the delayed single degree of freedom system equation by exponential matrix method(Elsevier Inc., 2014) Çevik M.; Mustafa Bahşi M.; Sezer M.In this paper, an exponential collocation method for the solution linear delay differential equations with constant delay is presented. The utility of this matrix based method is that it is very systematic and by writing a Maple program, any type of second order linear differential delay equation can be solved easily. The method is applied to three different types of delay equations; linear oscillator with delay (i) in the restoring force term, (ii) in the damping term, and (iii) in the acceleration term. Time response curves have been plotted for each type and the effect of the parameters of the delay terms has been shown. An error analysis based on residual function is carried out to show the accuracy of the results. © 2014 Elsevier Inc. All rights reserved.Item Numerical solution of pantograph-type delay differential equations using perturbation-iteration algorithms(Hindawi Publishing Corporation, 2015) Bahşi M.M.; Çevik M.The pantograph equation is a special type of functional differential equations with proportional delay. The present study introduces a compound technique incorporating the perturbation method with an iteration algorithm to solve numerically the delay differential equations of pantograph type. We put forward two types of algorithms, depending upon the order of derivatives in the Taylor series expansion. The crucial convenience of this method when compared with other perturbation methods is that this method does not require a small perturbation parameter. Furthermore, a relatively fast convergence of the iterations to the exact solutions and more accurate results can be achieved. Several illustrative examples are given to demonstrate the efficiency and reliability of the technique, even for nonlinear cases. © 2015 M. Mustafa Bahşi and Mehmet Çevik.Item Orthoexponential polynomial solutions of delay pantograph differential equations with residual error estimation(Elsevier Inc., 2015) Bahşi M.M.; Çevik M.; Sezer M.In this paper, a new matrix method based on orthogonal exponential (orthoexponential) polynomials and collocation points is proposed to solve the high-order linear delay differential equations with linear functional arguments under the mixed conditions. The convenience is that orthoexponential polynomials have shown to be effective in approximating a given function, fast and efficiently. An error analysis technique based on residual function is developed and applied to four problems to demonstrate the validity and applicability of the proposed method. It is confirmed that the present method yields quite acceptable results and the accuracy of the solution can significantly be increased by error correction and residual function. © 2015 Elsevier Inc. All rights reserved.Item Improved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equations(Springer Medizin, 2016) Bahşı M.M.; Kurt Bahşı A.; Çevik M.; Sezer M.This study is aimed to develop a new matrix method, which is used an alternative numerical method to the other method for the high-order linear Fredholm integro-differential-difference equation with variable coefficients. This matrix method is based on orthogonal Jacobi polynomials and using collocation points. The improved Jacobi polynomial solution is obtained by summing up the basic Jacobi polynomial solution and the error estimation function. By comparing the results, it is shown that the improved Jacobi polynomial solution gives better results than the direct Jacobi polynomial solution, and also, than some other known methods. The advantage of this method is that Jacobi polynomials comprise all of the Legendre, Chebyshev, and Gegenbauer polynomials and, therefore, is the comprehensive polynomial solution technique. © 2016, The Author(s).Item Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section(Elsevier Ltd, 2018) Sınır S.; Çevik M.; Sınır B.G.Nonlinear free and forced vibrations of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section are investigated. The beam has immovable, namely clamped-clamped and pinned-pinned boundary conditions, which leads to midplane stretching in the course of vibrations. Nonlinearities occur in the system due to this stretching. Damping and forcing terms are included after nondimensionalization. The equations are solved approximately using perturbation method and mode shapes by differential quadrature method. In the linear order natural frequencies and mode shapes are computed. In the nonlinear order, some corrections arise to the linear problem; the effect of these nonlinear correction terms on natural frequency is examined and frequency –response curves are drawn to show the unstable regions. In order to confirm the validity, our results are compared with others available in literature. © 2018Item Machine learning for the prediction of problems in steel tube bending process(Elsevier Ltd, 2024) Görüş V.; Bahşı M.M.; Çevik M.Tube bending is a widely used process in marine, automotive, construction and other industries. Different methods are available for this process during which various problems and defects are encountered. This paper aims to develop the most relevant model for bending the tubes using a computer numerical controlled (CNC) bending machine on the first attempt without any defects. To achieve this goal, the parameters affecting the tube bending process on the bending machine are defined. Based on these parameters, 150 bending experiments are conducted in an industrial plant to collect data and their results are used as dataset for machine learning (ML) algorithms. Seven different state-of-the-art ML algorithms –logistic regression, decision tree, k-nearest neighbor, random forest, Naïve Bayes, support vector machine and eXtreme gradient boosting (XGBoost)– are implemented using Python's Scikit-Learn library. Their performance is compared using confusion matrix and classification metrics such as accuracy, precision, recall, F1-score, receiver operating characteristic (ROC) curve and area under the ROC curve (AUC) value. Considering all the performance metrics, logistic regression performed best in terms of prediction on our dataset. XGBoost and support vector machine were quiet successful based on F1 score and AUC, respectively. Overall, logistic regression, Naïve Bayes, Support Vector Machine, and XGBoost showed performances above 90% across all metrics. Decision tree, k-nearest neighbor and random forest performed poorly compared to other algorithms for our data. The proposed ML method is expected to save costs by reducing material waste and labor time and to increase the process efficiency and the product quality. © 2024Item A Review of Polynomial Matrix Collocation Methods in Engineering and Scientific Applications(Springer Science and Business Media B.V., 2025) Çevik M.; Savaşaneril N.B.; Sezer M.Ordinary, partial, and integral differential equations are indispensable tools across diverse scientific domains, enabling precise modeling of natural and engineered phenomena. The polynomial collocation method, a powerful numerical technique, has emerged as a robust approach for solving these equations efficiently. This review explores the evolution and applications of the collocation method, emphasizing its matrix-based formulation and utilization of polynomial sequences such as Chebyshev, Legendre, and Taylor series. Beginning with its inception in the late 20th century, the method has evolved to encompass a wide array of differential equation types, including integro-differential and fractional equations. Applications span mechanical vibrations, heat transfer, diffusion processes, wave propagation, environmental pollution modeling, medical uses, biomedical dynamics, and population ecology. The method’s efficacy lies in its ability to transform differential equations into algebraic systems using orthogonal polynomials at chosen collocation points, facilitating accurate numerical solutions across complex systems and diverse engineering and scientific disciplines. This approach circumvents the need for mesh generation and simplifies the computational complexity associated with traditional numerical methods. This comprehensive review consolidates theoretical foundations, methodological advancements, and practical applications, highlighting the method’s pivotal role in modern computational mathematics and its continued relevance in addressing complex scientific challenges. © The Author(s) 2025.