Browsing by Author "Demir, DD"

Now showing 1 - 17 of 17
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    Strengthening of reinforced concrete beams using external steel members
    Demir, A; Ercan, E; Demir, DD
    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.
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    Pell-Lucas series approach for a class of Fredholm-type delay integro-differential equations with variable delays
    Demir, DD; Lukonde, AP; Kürkçü, ÖK; Sezer, M
    In this study, a Pell-Lucas matrix-collocation method is used to solve a class of Fredholm-type delay integro-differential equations with variable delays under initial conditions. The method involves the basic matrix structures gained from the expansions of the functions at collocation points. Therefore, it performs direct and immediate computation. To test its advantage on the applications, some numerical examples are evaluated. These examples show that the method enables highly accurate solutions and approximations. Besides, the accuracy of the solutions and the validity of the method are checked via the residual error analysis and the upper bound error, respectively. Finally, the numerical results, such as errors and computation time, are compared in the tables and figures.
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    DYNAMICAL BEHAVIOR OF AN AXIALLY MOVING STRING CONSTITUTED BY A FRACTIONAL DIFFERENTIATION LAW
    Demir, DD; Sinir, BG; Bildk, N
    In this paper, the dynamical behavior of an axially moving string modeled by fractional derivative is investigated. The governing equation represented motion is solved by the method of multiple scales. Considering principal parametric resonance, the stability boundaries for string with simple supports are obtained. Numerical results indicate the effects of fractional damping on stability.
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    Application of fractional calculus in the dynamics of beams
    Demir, DD; Bildik, N; Sinir, BG
    This paper deals with a viscoelastic beam obeying a fractional differentiation constitutive law. The governing equation is derived from the viscoelastic material model. The equation of motion is solved by using the method of multiple scales. Additionally, principal parametric resonances are investigated in detail. The stability boundaries are also analytically determined from the solvability condition. It is concluded that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations.
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    Linear dynamical analysis of fractionally damped beams and rods
    Demir, DD; Bildik, N; Sinir, BG
    The aim of this study is to develop a general model for beams and rods with fractional derivatives. Fractional time derivatives can represent the damping term in dynamical models of continuous systems. Linear differential operators with spatial derivatives make it possible to generalize a wide range of problems. The method of multiple scales is directly applied to equations of motion. For the approximate solution, the amplitude and phase modulation equations are obtained in terms of the operators. Stability boundaries are derived from the solvability condition. It is shown that a fractional derivative influences the stability boundaries, natural frequencies, and amplitudes of vibrations. The solution procedure may be applied to many problems with linear vibrations of continuous systems.
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    Determining Critical Load in the Multispan Beams with the Nonlinear Model
    Demir, DD; Sinir, BG; 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.
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    The Combination Resonance Analysis for an Axially Moving String
    Demir, DD; Sinir, BG; 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.
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    Linear vibrations of continuum with fractional derivatives
    Demir, DD; Bildik, N; Sinir, BG
    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.
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    The Solution of a String Model by Adomian Decomposition Method
    Demir, DD; 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.
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    The Shooting Method for the Second Order Singularly Perturbed Differential Equation
    Demir, DD; 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.
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    The Numerical Solution of Fractional Bratu-Type Differential Equations
    Demir, DD; Zeybek, A
    This paper introduce the differential transform method (DTM) to solve the fractional Bratu-type differential equation modeling a combustion in numerical slab. For the definition of fractional derivative, the Caputo sense is used. The result corresponds to the exact solution when the obtained solution is constructed as power series for some values of fractional order. Finally, some examples are presented to indicate the efficiency of applied method. Comparison of the results obtained by DTM with those obtained by other methods is given.
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    Perturbed trapezoid inequalities for n th order differentiable convex functions and their applications
    Demir, DD; Sanal, 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.
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    THE SOLUTION OF LATERAL HEAT LOSS PROBLEM USING COLLOCATION METHOD WITH CUBIC B-SPLINES FINITE ELEMENT
    Bildik, N; Demir, DD
    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.
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    The analysis of nonlinear vibrations of a pipe conveying an ideal fluid
    Sinir, BG; Demir, DD
    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. (C) 2015 Elsevier Masson SAS. All rights reserved.
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    Dynamical analysis of the general beam model with singularity function
    Demir, DD; Sinir, BG; Kahraman, E
    The aim of this study is to present a general model with variable coefficients corresponding to some structural elements such as beam, string, bar, and rod. To solve general model with variable coefficients, a different solution procedure combining a method of multiple scales (MINIS) and a finite difference method (FDM) is presented in this study. This technique provides an advantage in the numerical solution of the structural element model containing any discontinuity and in its dynamical analysis by perturbation method. Furthermore, two problems including discontinuity are considered to show the accuracy of the method presented. The comparisons of the numerical results obtained from the proposed method and classical method are introduced.
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    Pell-Lucas polynomial method for Volterra integral equations of the second kind
    Lukonde, AP; Demir, DD; 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.