Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Displacement Analysis of Non-Circular Planar Curved Beams Under In-Plane Impulsive Load(Izmir Institute of Technology, 2015) Çelik, Ahmet; Yardımoğlu, BülentIn this study, time response of a planar curved beam with variable curvatures under in-plane impact load is analyzed by two numerical methods which are Finite Difference and Finite Element Methods. The solution procedures in both methods are based on solution of eigenvalue and time response problems. Catenary form is selected as the axis of curved beam. A computer program is developed in Mathematica for the solution with Finite Difference Method. Moreover, a computer code is written for the geometric and finite element models of curved beam with variable curvature in ANSYS by using APDL (ANSYS Parametric Design Language). Solutions of the two methods are compared in each other and then good agreement is observed. The effects of impuls and damping properties on the time response are investigated.Master Thesis Vibration Analysis of Rotating Curved Beams With Variable Cross-Section(Izmir Institute of Technology, 2014) Kartav, Osman; Yardımoğlu, BülentIn this study, in-plane free vibration characteristics of rotating curved beams are investigated by Finite Difference Method and Finite Element Method since the mathematical model of the present problem is based on the differential eigenvalue problem with variable coefficients. A computer program regarding the titled problem is developed in Mathematica and this program is verified by using results available in the literature. The effects of taper parameters of the curved beam and rotation speed on natural frequencies are investigated.Master Thesis Conjugate Natural Convection Heat Transfer in a Cavity With Finite Wall Thickness(Izmir Institute of Technology, 2009) Hakyemez, Erinç; Mobedi, MoghtadaThe effects of a heat barrier, located in the thick ceiling wall of a square enclosure, on conjugate conduction and natural convection heat transfer are investigated numerically. The analysis is performed by numerical solution of the continuity, unsteady momentum conservation and energy equations with finite difference solution method based on the streamfunction-vorticity formulation. The vertical walls of the enclosure are differentially heated and horizontal walls are adiabatic. A thin heat barrier, having infinite thermal resistance, is located in the ceiling wall at different locations. The calculations are made for different Rayleigh numbers (103 Ra 106), thermal conductivity ratios (1 K 100), dimensionless locations of heat barrier (0<Xh<1) and two dimensionless ceiling wall thicknesses (D . 0.05 and D . 0.20). By using the results of the computer program, streamlines and isotherms are plotted. Heatline visualization technique is used to simulate heat transport and the effect of heat barrier is presented by comparing and plotting heatlines for the cavity and for the solid region with and without heat barrier. The study is performed for air with Prandtl number 0.71. It is found that the effect of heat barrier is more significant in the cavity with high thermal conductivity ratio but low Rayleigh number. There are certain reductions in the average Nusselt number at the vertical walls of the cavity and dimensionless heat transfer rate of the solid region walls for high conductivity ratios, but the reduction in dimensionless heat transfer rate is greater.Master Thesis Free Vibration Analysis of Curved Beams With Variable Radii of Curvature on Elastic Foundations(Izmir Institute of Technology, 2013) Çelebi, Sanal; Yardımoğlu, BülentFree out of plane vibration characteristics of curved beams with variable curvature on elastic foundation are studied by Finite Difference Method (FDM) since the mathematical model of the present system based on the coupled differential eigenvalue problem with variable coefficients. Firstly, vibrations of beams on different elastic foundations are reviewed. Then, out of plane vibrations of curved beams on different elastic foundations are investigated. FDM is detailed for this study. To solve the coupled differential eigenvalue problem, FDM is examined with several computer programs developed in Mathematica. The effects of curvature of the curved beams and elastic foundation parameters on natural frequencies are investigated. The accuracy of the present results obtained from the developed program is evaluated by comparing with FEM results found from model created in ANSYS.Master Thesis An Application of the Finite Differences Method To a Dynamical Interface Problem(Izmir Institute of Technology, 2004) Ağıroğlu, İzzet Onur; Tanoğlu, GamzeA multiple-order-parameter model for Cu-Au system on a face cubic centered lattice was recently developed in the presence of anisotropy. In that model, three order parameters (non-conserved) and one concentration order parameter (conserved), which has been taken as a constant, were considered. Later on, the model has been extended, so that, concentration has been taken as a variable. It has been seen that two models were in a good agreement near critical temperature since the non-conserved order parameter behaves like a constant near critical temperature in both models. Thus, we extended the rst model to a dynamical diffuse interface model near critical temperature. After writing the free energy of the system in terms of the order parameters, minimizing the energy with respect to the order parameters and Langevin equation yield the non-linear system of parabolic equations. The finite differences method was implemented to solve this non-linear system of parabolic equations. The forward difference discretization was applied for the rst derivative of the solution with respect to time and centered difference discretization was applied for the second order derivative of the solution with respect to spatial variable. We obtained stability criteria and nd the error bound. The orientation dependence proles, variation of interfacial energy and the effect of the degree of the anisotropy on the width of the diffuse interface are simulated when the time evolves.Master Thesis Analysis of Finite Difference Methods for Convection-Diffusion Problem(Izmir Institute of Technology, 2004) Demirayak, Murat; Neslitürk, Ali İhsanWe consider finite difference methods for one dimensional convection diffusion problem. An error analysis shows that the solution of the upwind scheme is not uniformly convergent in the discrete maximum norm due to its behavior in the layer. Then, we introduce and analyze a numerical method, Il.inAllen-Southwell scheme, that is first-order uniformly convergent in the discrete maximum norm throughout the domain. Finally, we present numerical results that confirm theoretical findings.Master Thesis The Solution of Some Differential Equations by Nonstandard Finite Difference Method(Izmir Institute of Technology, 2005) Kıran Güçoğlu, Arzu; Tanoğlu, GamzeIn this thesis, the nonstandard finite difference method is applied to construct thenew finite difference equations for the first order nonlinear dynamic equation, second order singularly perturbed convection diffusion equation and nonlinear reaction diffusion partial differential equation The new discrete representation for the first order nonlinear dynamic equation allows us to obtain stable solutions for all step-sizes.For singularly perturbed convection diffusion equation, the error analysis reveals that the nonstandard finite difference representation gives the better results for any values of the perturbation parameters. Finally, the new discretization for the last equation is obtained.The lemma related to the positivity and boundedness conditions required for the nonstandard finite difference scheme is stated. Numerical simulations for all differential equarions are illustrated based on the parameters we considered.