Browsing by Author "Sinir B.G."
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Item Bifurcation and Chaos of slightly curved pipes(Association for Scientific Research, 2010) Sinir B.G.Non-linear vibrations of slightly curved pipes conveying fluid with constant velocity are investigated. The curvature is taken as an arbitrary function of the spatial variable. The initial displacement is considered due to the geometry of the pipe itself. The ends of the curved pipe are assumed to be immovable simple supports. The equations of motion of pipes are derived using Hamilton's principle and solved by Galerkin method. The bifurcation diagrams are presented for various amplitudes of the curvature function and fluid velocity. The periodic and chaotic motions have been observed in the transverse vibrations of slightly curved pipe conveying fluid. © Association for Scientific Research.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 Exact solution and buckling configuration of nanotubes containing internal flowing fluid(Association for Scientific Research, 2013) Sinir B.G.; Uz F.E.; Ergun S.In this study, the post-divergence behaviour of nanotubes of conveying internal moving fluid with both inner and outer surface layers are analyzed in nonlinear theorical model. The governing equation has the cubic nonlinearity. The source of this nonlinearity is the surface effect and mid-plane stretching in the nanobeam theory. Exact solutions for the post buckling configurations of nanotubes with clamped-hinged with torsionally spring and hybrid boundary conditions is found. The critical flow velocity at which the nanotube is buckled is shown. The effects of various non-dimensional system parameters on the post-buckling behaviour are investigated.Item Buckling configurations and dynamic response of buckled euler-bernoulli beams with non-classical supports(Brazilian Association of Computational Mechanics, 2014) Sinir B.G.; Özhan B.B.; Reddy J.N.Exact solutions of buckling configurations and vibration response of post-buckled configurations of beams with non-classical boundary conditions (e.g., elastically supported) are presented using the Euler-Bernoulli theory. The geometric nonlinearity arising from mid-plane stretching (i.e., the von Kármán nonlinear strain) is considered in the formulation. The nonlinear equations are reduced to a single linear equation in terms of the transverse deflection by eliminating the axial displacement and incorporating the nonlinearity and the applied load into a constant. The resulting critical buckling loads and their associated mode shapes are obtained by solving the linearized buckling problem analytically. The buckling configurations are determined in terms of the applied axial load and the transverse deflection. The first buckled shape is the only stable equilibrium position for all boundary conditions considered. Then the pseudo-dynamic response of buckled beams is also determined analytically. Natural frequency versus buckling load and natural frequency versus amplitudes of buckling configurations are plotted for various non-classical boundary conditions. © 2014, Brazilian Association of Computational Mechanics. All rights reserved.Item Comments on "asymptotic analysis of an axially viscoelastic string constituted by a fractional differentiation law"(2014) Sinir B.G.In this comment, some remarks are made on the paper "Asymptotic analysis of an axially viscoelastic string constituted by a fractional differentiation law" by Tianzhi Yang, Bo Fang, published in the International Journal of Non-Linear Mechanics 49 (2013) 170-174. © 2013 Elsevier Ltd.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 Dynamical behavior of an axially moving string constituted by a fractional differentiation law(Shiraz University, 2015) Dönmez Demir D.; Sinir B.G.; Bildik 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. © Shiraz University.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 THE SOLUTION OF THE GOVERNING EQUATION OF THE BEAM ON LINEAR SPRING FOUNDATION MODELED BY A DISCONTINUITY FUNCTION(Yildiz Technical University, 2019) DÖNMEZ Demır D.; Sinir B.G.; Kahraman E.The structural engineering researches have attracted considerable attention by many scientist for several decades. Determining the dynamical behaviors of structural elements with some discontinuous is of great importance in many engineering applications. The mentioned structures can be modelled two different ways. In the first approximation so-called the classical approach, a fourth order differential equation are written for each part of beam separated in the distinct discontinuity locations. Therefore, we obtain a system of equation containing n + 1 number of the differential equation with boundary and transient conditions. Secondly, the real problem can be reformulated by only one differential equation having discontinuity function. In this study, we introduce the method of multiple scales as the solution technique. Since we encountered by the differential equation with discontinuity function in the part of order discretization during the perturbative solution, we have used a numerical technique for the solution. The mentioned technique is applied on the beam model lying on lineer spring foundation called as Winkler type foundation. © 2019 Yildiz Technical University. All Rights Reserved.Item Semi-identical Solution to Nonlinear Euler-Bernouilli Beam Model(Institute of Electrical and Electronics Engineers Inc., 2019) Yildiz B.; Sinir B.G.; Sinir S.In this study, the Euler-Bernoulli beam model is considered. It is analyzed with geometric nonlinearity. Solution of the mathematical model is obtained with semi-analytical method. © 2019 IEEE.Item Dynamical analysis of the general beam model with singularity function(University of Kuwait, 2021) Dönmez Demir D.; Sinir B.G.; 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 (MMS) 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. © 2021 University of Kuwait. All rights reserved.Item Derivation of Governing Equations by Using Vector Approach and Comparison of Analytical Solutions of Post-buckling Behaviors of Transverse Functionally Graded Shear Deformable Beam Theories(Institute for Ionics, 2023) Sinir B.G.In this study, the post-buckling behavior of a transverse functionally graded beam is investigated. Euler–Bernoulli beam theory (EBT) and shear deformable beam theories are taken into account in deriving the mathematical models of the beam using the vector approach. Timoshenko theory (TBT) and six different higher order beam theories (HOBT), namely Reddy, Touratier, Soldatos, Karma, Akavcı and Violet, are considered as shear deformable beam theories. It has been shown that mathematical models of shear deformable beam theories can be obtained using the vector approach. There are two different models developed for shear deformable beam theories depending on normal and shear forces and moment. It is found that the model which is named as Model 2 in this study yield inappropriate results. The functionally graded materials are characterized by using power law functions. The non-dimensional integro-non-linear differential equations system is solved analytically. The critical load values calculated for EBT, TBT and HOBT theories depending on different material conditions and slenderness ratio values are presented in tables. In addition, pitchfork bifurcation diagrams are drawn showing the post-buckling behavior of the beam. In addition, the regions where the examined beam theories are valid depending on the slenderness coefficient are shown. © 2022, King Fahd University of Petroleum & Minerals.