Browsing by Author "Boyaci, H"

Now showing 1 - 20 of 26
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    STRENGTH OF WHEAT AND BARLEY STEMS AND DESIGN OF NEW BEAM/COLUMNS
    Deger, G; Pakdemirli, M; Candan, F; Akgün, S; Boyaci, H
    In this study, physical and mechanical properties of wheat and barley stems are examined. Transverse sections of the stems are magnified by a microscope and the material structure in the transverse sections are analysed with image processing programs. Geometric properties such as inner, outer radius, stern wall thickness and density variation of the material along the radius are measured and density variations are approximated by a mathematical model. Moment of inertia of the cross-sectional area which plays a vital role in resistance against bending and buckling is calculated approximately. Using the material density variations of the wheat (Triticum sativum L.) stems, new beam/columns are designed. Stress distributions in this new design and conventional designs of equivalent weight are compared using ANSYS program. It is found that stresses are more uniformly distributed in the new design with maximum stresses being lower than the conventional designs.
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    New perturbation-iteration solutions for nonlinear heat transfer equations
    Aksoy, Y; Pakdemirli, M; Abbasbandy, S; Boyaci, H
    Purpose - The purpose of this paper is to apply, for the first time, the authors' newly developed perturbation iteration method to heat transfer problems. The effectiveness of the new method in nonlinear heat transfer problems will be tested. Design/methodology/approach - Nonlinear heat transfer problems are solved by perturbation iteration method. They are also solved by the well-known technique variational iteration method in the literature. Findings - It is found that perturbation iteration solutions converge faster to the numerical solutions. More accurate results can be achieved with this new method for nonlinear heat transfer problems. Research limitations/implications - A few iterations are actually sufficient. Further iterations need symbolic packages to calculate the solutions. Practical implications - This new technique can practically be applied to many heat and flow problems. Originality/value - The new perturbation iteration technique is successfully implemented to nonlinear heat transfer problems. Results show good agreement with the direct numerical simulations and the method performs better than the existing variational iteration method.
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    Nonlinear vibrations of axially moving beams with multiple concentrated masses Part I: primary resonance
    Sarigül, M; Boyaci, H
    Transverse vibrations of axially moving beams with multiple concentrated masses have been investigated. It is assumed that the beam is of Euler-Bernoulli type, and both ends of it have simply supports. Concentrated masses are equally distributed on the beam. This system is formulated mathematically and then sought to find out approximately solutions of the problem. Method of multiple scales has been used. It is assumed that axial velocity of the beam is harmonically varying around a mean-constant velocity. In case of primary resonance, an analytical solution is derived. Then, the effects of both magnitude and number of the concentrated masses on nonlinear vibrations are investigated numerically in detail.
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    Effects of non-ideal boundary conditions on vibrations of microbeams
    Ekici, HO; Boyaci, H
    Effects of non-ideal boundary conditions on the vibrations of microbeams are investigated. Stretching effect as well as axial force is included along with the non-ideal boundary conditions. The Method of Multiple Time Scales (a perturbation technique) is employed to solve the non-dimensional equation of motion for subharmonic and superharmonic resonance cases. The frequencies and mode shapes obtained are compared with the ideal boundary conditions case and the differences between them are contrasted on frequency response curves.
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    Nonlinear vibrations of axially moving multi-supported strings having non-ideal support conditions
    Yurddas, A; Özkaya, E; Boyaci, H
    In this study, nonlinear vibrations of an axially moving multi-supported string have been investigated. The main difference of this study from the others is in that there are non-ideal supports allowing minimal deflections between ideal supports at both ends of the string. Nonlinear equations of the motion and boundary conditions have been obtained using Hamilton's Principle. Dependence of the equations of motion and boundary conditions on geometry and material of the string have been eliminated by non-dimensionalizing. Method of multiple scales, a perturbation technique, has been employed for solving the equations of motion. Axial velocity has been assumed a harmonically varying function about a constant value. Axially moving string has been investigated in three regions. Vibrations have been examined for three different cases of the velocity variation frequency. Stability has been analyzed and stability boundaries have been established for the principal parametric resonance case. Effects of the non-ideal support conditions on stability boundaries and vibration amplitudes have been investigated.
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    Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass
    Özkaya, E; Sarigül, M; Boyaci, H
    In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlinear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of multiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequencies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.
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    A comparison of different versions of the method of multiple scales for partial differential equations
    Boyaci, H; Pakdemirli, M
    Applications of the methods of multiple scales (a perturbation method) to partial differential systems arising in non-linear vibrations of continuous systems are considered. Two different versions of the method of multiple scales are applied to two general non-linear models. In one of the models, the small parameter (epsilon) multiplies an arbitrary non-linear cubic operator whereas in the other model, arbitrary quadratic and cubic non-linearities exist. The linear parts of both models are represented by arbitrary operators. General solutions are found by applying different versions of the method of multiple scales. Results of the first version (reconstitution method) and the second version (proposed by Rahman and Burton [8]) are compared for both models. From the comparisons of both methods, it is found that the second version yields better results. Applications of the general models to specific problems are also presented. A final recommendation is to use the second version of the method of multiple scales combined with the direct-perturbation method in finding steady state solutions of partial differential equations. (C) 1997 Academic Press Limited.
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    Non-linear vibrations of a simple-simple beam with a non-ideal support in between
    Pakdemirli, M; Boyaci, H
    A simply supported Euler-Bernoulli beam with an intermediate support is considered. Non-linear terms due to immovable end conditions leading to stretching of the beam are included in the equations of motion. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the intermediate support is assumed to allow small deflections. An approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique. Ideal and non-ideal frequencies as well as frequency-response curves are contrasted. (C) 2003 Elsevier Ltd. All rights reserved.
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    Nonlinear vibrations and stability analysis of axially moving strings having nonideal mid-support conditions
    Yurddas, A; Özkaya, E; Boyaci, H
    In this study, nonlinear vibrations of an axially moving string are investigated. The main difference of this study from other studies is that there is a nonideal support between the opposite sides, which allows small displacements. Nonlinear equations of motion and boundary conditions are derived using Hamilton's principle. Equations of motion and boundary conditions are converted to nondimensional form. Thus, the equations become independent from geometry and material properties. The method of multiple scales, a perturbation technique, is used. A harmonically varying velocity function is chosen for modeling the axial movement. String as a continuous medium is investigated in two regions. Vibrations are investigated for three different cases of the excitation frequency . Stability analysis is carried out for these three cases, and stability boundaries are determined for the principle parametric resonance case. Thus, differences between ideal and nonideal boundary conditions are investigated.
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    Beam vibrations with non-ideal boundary conditions
    Boyaci, H
    A simply supported damped Euler-Bernoulli beam with immovable end conditions is considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deflections and moments. Approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique.
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    Generation of root finding algorithms via perturbation theory and some formulas
    Pakdemirli, M; Boyaci, H
    Perturbation theory is systematically used to generate root finding algorithms. Depending on the number of correction terms in the perturbation expansion and the number of Taylor expansion terms, different root finding formulas can be generated. The way of separating the resulting equations after the perturbation expansion alters the root-finding formulas also. Well known cases such as Newton-Raphson and its second correction, namely the Householder's iteration, are derived as examples. Moreover, higher order algorithms which may or may not be the corrections of well known formulas are derived. The formulas are contrasted with each other as well as with some new algorithms obtained by modified Adomian Decomposition Method proposed in Ref. [S. Abbasbandy, Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method, Applied Mathematics and Computation 145 (2003) 887-893]. (c) 2006 Elsevier Inc. All rights reserved.
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    Non-linear vibrations and stability of an axially moving beam with time-dependent velocity
    Öz, HR; Pakdemirli, M; Boyaci, H
    Non-linear vibrations of an axially moving beam are investigated. The non-linearity is introduced by including stretching effect of the beam. The beam is moving with a time-dependent velocity, namely a harmonically varying velocity about a constant mean velocity. Approximate solutions are sought using the method of multiple scales. Depending on the variation of velocity, three distinct cases arise: (i) frequency away from zero or two times the natural frequency, (ii) frequency close to zero, (iii) frequency close to two times the natural frequency. Amplitude-dependent non-linear frequencies are derived. For frequencies close to two times the natural frequency, stability and bifurcations of steady-state solutions are analyzed. For frequencies close to zero, it is shown that the amplitudes are bounded in time. (C) 2000 Elsevier Science Ltd. All rights reserved.
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    Transverse vibrations of tensioned pipes conveying fluid with time-dependent velocity
    Öz, HR; Boyaci, H
    In this study, the transverse vibrations of highly tensioned pipes with vanishing flexural stiffness and conveying fluid with time-dependent velocity are investigated. Two different cases, the pipes with fixed-fixed end and fixed-sliding end conditions are considered. The time-dependent velocity is assumed to be a harmonic function about a mean velocity. These systems experience a Coriolis acceleration component which renders such systems gyroscopic. The equation of motion is derived using Hamilton's principle and solved analytically by direct application of the method of multiple scales (a perturbation technique). The natural frequencies are found. Increasing the ratio of fluid mass to the total mass per unit length increases the natural frequencies. The principal parametric resonance cases are investigated in detail. Stability boundaries are determined analytically. It is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system. When the velocity fluctuation frequency is close to zero, no instabilities are detected up to the first order of perturbation. Numerical results are presented for the first two modes. (C) 2000 Academic Press.
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    Nonlinear Transverse Vibrations of a Slightly Curved Beam resting on Multiple Springs
    Özkaya, E; Sarigül, M; Boyaci, H
    In this study, nonlinear vibrations of a slightly curved beam of arbitrary rise functions is handled in case it rests on multiple springs. The beam is simply supported on both ends and is restricted in longitudinal directions using the supports. Thus, the equations of motion have nonlinearities due to elongations during vibrations. The method of multiple scales (MMS), a perturbation technique, is used to solve the integro-differential equation analytically. Primary and 3 to 1 internal resonance cases are taken into account during steady-state vibrations. Assuming the rise functions are sinusoidal in numerical analysis, the natural frequencies are calculated exactly for different spring numbers, spring coefficients, and spring locations. Frequency-amplitude graphs and frequency-response graphs are plotted by using amplitude-phase modulation equations.
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    A new perturbation technique in solution of nonlinear differential equations by using variable transformation
    Elmas, N; Boyaci, H
    A perturbation algorithm using a new variable transformation is introduced. This transformation enables control of the independent variable of the problem. The problems are solved with new transformation: Classical Duffing equation with cubic nonlinear term and a singular perturbation problem. Results of multiple scales, Lindstedt Poincare method, new method and numerical solutions are contrasted. (C) 2013 Elsevier Inc. All rights reserved.
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    A NEW PERTURBATION ALGORITHM WITH BETTER CONVERGENCE PROPERTIES: MULTIPLE SCALES LINDSTEDT POINCARE METHOD
    Pakdemirli, M; Karahan, MMF; Boyaci, H
    A new perturbation algorithm combining the Method of Multiple Scales and Lindstedt-Poincare techniques is proposed for the first time. The algorithm combines the advantages of both methods. Convergence to real solutions with large perturbation parameters can be achieved for both constant amplitude and variable amplitude cases. Three problems are solved: Linear damped vibration equation, classical duffing equation and damped cubic nonlinear equation. Results of Multiple Scales, new method and numerical solutions are contrasted. The proposed new method produces better results for strong nonlinearities.
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    Vibrations of stretched damped beams under non-ideal boundary conditions
    Boyaci, H
    A simply Supported damped Euler-Bernoulli beam with immovable end conditions are considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deflections and moments. Approximate analytical Solution of the problem is found using the method of multiple scales, a perturbation technique.
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    The validation of the Turkish version of Asthma Control Test (vol 22, pg 1773, 2013)
    Uysal, MA; Mungan, D; Yorgancioglu, A; Yildiz, F; Akgun, M; Gemicioglu, B; Turktas, H; Ozkan, G; Yilmaz, I; Incioglu, M; Boyaci, H; Atis, S; Yalcin, A; Bayram, NG; Deveci, F; Pulur, D; Ozgur, ES; Dursun, B; Bulbul, Y; Sulu, E; Yilmaz, V