Browsing by Author "Demir D.D."
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Item The solution of lateral heat loss problem using collocation method with cubic B-splines finite element(2012) Bildik N.; Demir D.D.This paper deals with the solutions of lateral heat loss equation by using collocation method with cubic B-splines finite elements. The stability analysis of this method is investigated by considering Fourier stability method. The comparison of the numerical solutions obtained by using this method with the analytic solutions is given by the tables and the figure. © (2012) Trans Tech Publications, Switzerland.Item Linear vibrations of continuum with fractional derivatives(2013) Demir D.D.; Bildik N.; Sinir B.G.In this paper, linear vibrations of axially moving systems which are modelled by a fractional derivative are considered. The approximate analytical solution is obtained by applying the method of multiple scales. Including stability analysis, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted by graphs. It is determined that the external excitation force acting on the system has an effect on the stiffness of the system. Moreover, the general algorithm developed can be applied to many problems for linear vibrations of continuum. © 2013 Donmez Demir et al.; licensee Springer.Item The combination resonance analysis for an axially moving string(2013) Demir D.D.; Sinir B.G.; Bildik N.In this paper, the vibrations of an initially stressed moving string with fractional damping are investigated. Traveling string with two modes are considered and the approximate analytical solutions are obtained by using the method of multiple scales. The stability boundaries are analytically determined. Consequently, it is found that instability appears when the frequency is close to the sum or difference of any two natural frequencies. © 2013 AIP Publishing LLC.Item Preface of the "symposium on some new trends in nonlinear differential equations"(American Institute of Physics Inc., 2015) Bildik N.; Demir D.D.[No abstract available]Item The solution of a string model by adomian decomposition method(American Institute of Physics Inc., 2015) Demir D.D.; Koca E.Adomian Decomposition Method for the dimensionless axially accelerating string is proposed in this paper. The velocity is assumed as a constant mean velocity. The influence of the velocity on the displacement of the string is numerically discussed. © 2015 AIP Publishing LLC.Item The analysis of nonlinear vibrations of a pipe conveying an ideal fluid(Elsevier Ltd, 2015) Sinir B.G.; Demir D.D.In this study, the non-linear vibrations of fixed-fixed tensioned pipe with vanishing flexural stiffness and conveying fluid with constant velocity are considered. The fractional calculus approach is introduced in the constitutive relationship of viscoelastic material. The pipe is on fixed support and the immovable end conditions result in the extension of the pipe during vibration and hence are introduced further nonlinear terms to the equation of motion. Analytical solutions are obtained by using the method of multiple scales. Nonlinear frequencies versus the amplitude of deflection are calculated. For frequencies close to one times the natural frequency, stability of steady-state solutions is analysed. © 2015 Elsevier Masson SAS. All rights reserved.Item The shooting method for the second order singularly perturbed differential equation(American Institute of Physics Inc., 2016) Demir D.D.; Koca E.In this study, we introduce the solution of the second order singularly perturbed differential equation. The shooting method will be used to obtain the series solution. The variation of the approximate solution for the nonhomogeneous equation is illustrated. © 2016 Author(s).Item (I.) applications of mathematical methods and models in sciences and engineering(American Institute of Physics Inc., 2016) Bildik N.; Demir D.D.; Pandlr Y.[No abstract available]Item Determining critical load in the multispan beams with the nonlinear model(American Institute of Physics Inc., 2017) Demir D.D.; Sinir B.G.; Usta L.The beams which are one of the most commonly used structural members are quite important for many researchers. Mathematical models determining the response of beams under external loads are concluded from elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. In this study, the derivation of the nonlinear model is introduced to determine the critical load in the multispan beams. Since the engineering practice of this kind of problems is very common, determining the critical load is quite important. For this purpose, the nonlinear mathematical model of the multispan Euler-Bernoulli beam is firstly obtained. To be able to obtain the independent of the material and the geometry, the present model are became dimensionless. Then, the critical axial load can be determined via the nonlinear solution of the governing equation. © 2017 Author(s).Item Strengthening of reinforced concrete beams using external steel members(Techno Press, 2018) Demir A.; Ercan E.; Demir D.D.The objective of this study is to devise an alternative strengthening method to the ones available in the literature. So, external steel members were used to enhance both flexural and shear capacities of reinforced concrete (RC) beams having insufficient shear capacity. Two types of RC beams, one without stirrups and one with lacking stirrups, were prepared in the study. These beams were strengthened with external steel clamps devised by the authors and with external longitudinal reinforcements. Although the use of clamps alone didn’t have a significant effect on the load carrying capacity of the tested beams, the ductility increased approximately tenfold and the failure behavior changed from brittle to ductile. Although the use of clamps and longitudinal reinforcements together did not significantly increase the ductility of the beams, it approximately doubled their load capacities. The results of the experimental study were compared to the ones obtained from nonlinear finite element analysis (NLFEA) and it was observed that they were compatible. Finally, it can be concluded that the devised method could be applied to structural members as an alternative to methods in application due to lightness, low-cost, easy applicable and reliable. Copyright © 2018 Techno-Press, Ltd.Item Perturbed trapezoid inequalities for n th order differentiable convex functions and their applications(American Institute of Mathematical Sciences, 2020) Demir D.D.; Şanal G.In this study, we introduce a new general identity for n th order differentiable functions. Also, we establish some new inequalities regarding general perturbed trapezoid inequality for the functions whose the absolute values of n th derivatives are convex. Finally, some applications for special means are provided. © 2020 the Author(s), licensee AIMS Press.Item Pell–Lucas polynomial method for Volterra integral equations of the second kind(Springer Science and Business Media Deutschland GmbH, 2023) Lukonde A.P.; Demir D.D.; Emadifar H.; Khademi M.; Azizi H.This paper introduces a Pell-Lucas collocation method for solving Volterra integral equations of the second kind. The proposed method employs collocation points and represents Pell–Lucas polynomials and their derivatives in matrix vector form. By utilizing this approach, Volterra integral equations are converted into a matrix equation, wherein the undetermined coefficients correspond to the Pell–Lucas coefficients. The effectiveness and efficiency of the proposed method are demonstrated through numerical examples, which yield accurate solutions. The accuracy of these solutions is further assessed using absolute and residual error analysis. Moreover, the obtained numerical results obtained via the Pell–Lucas collocation method are compared with analytical solutions in tables and figures, thus providing a comprehensive evaluation of the method's performance. © 2023, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.