Uğur Yücel

Homotopy analysis method for the sine-Gordon equation with initial conditions

In this work, approximate analytical solution of the sine-Gordon equation with initial conditions is obtained by the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. It is shown that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions.

Calculation of leakage and dynamic coefficients of stepped labyrinth gas seals

Rotor-fluid interactions can cause self-excited vibrations in high-density turbomachines. One of the most important sources for excitation is the flow through labyrinth seals. The gas flow through the seals creates net pressure and shear forces acting on the rotor. It is necessary to predict these forces exactly for reliably operating turbomachines. The labyrinth seal forces are characterized by rotordynamic coefficients. This paper presents a theoretical work on the calculation of leakage and dynamic coefficients for stepped labyrinth gas seals. The continuity and circumferential momentum equations are given for compressible flow in a stepped labyrinth seal. Periodic and analytic solutions of these equations are obtained for the case of time dependent flow generated by a non-axisymmetric rotation of the rotor using an axisymmetric solution based on different assumption about the flow coefficient. The rotordynamic coefficients are then calculated and the results of this analysis are compared with relatively recent experimental data.

Differential quadrature method (DQM) for a class of singular two-point boundary value problems

Differential quadrature method is applied in this work to solve singular two-point boundary value problems with a linear or non-linear nature. It is demonstrated through numerical examples that accurate results for the problem with different types of boundary conditions can be obtained using a considerably small number of grid points. The relative, root mean square and maximum absolute errors in computed solutions are given to show the performance of the method.

Free Vibration Analysis of the Laminated Composite Beams by Using DQM

In this study, the effects of stacking sequences of composite laminated beams on natural frequencies are investigated using the differential quadrature method (DQM). DQM is an efficient discretization technique for obtaining accurate numerical solutions to initial and/or boundary value problems using a considerably small number of grid points. In this way, a theoretical DQM model for the laminated composite beam has been developed. Some of the results obtained from DQM are compared with the results obtained experimentally. Then, these results are compared with the numerical and experimental results available in the literature. It has been seen that all of the results considered are very close to each other. It has also been concluded that the effective stiffness of the laminated composite beam can be altered through a change in the stacking sequence. This allows tailoring of the material to achieve desired natural frequencies and respective mode shapes without changing its geometry drastically or without increasing its weight.

Numerical approximations of Sturm–Liouville eigenvalues using Chebyshev polynomial expansions method

Abstract In this paper, an efficient technique based on the Chebyshev polynomial expansions for computing the eigenvalues of second- and fourth-order Sturm–Liouville boundary value problems is proposed. This technique reduces the given Sturm–Liouville problem to an integral equation. The resulting integral equation is then transformed into the eigenvalue equation by calculating the integrals at the grid points using the Chebyshev expansions. Thus, the required eigenvalues of the given problem are obtained by solving this eigenvalue equation. The excellent performance of this scheme is illustrated through some numerical examples, and comparison with other methods is presented.

Comparative Analysis of Free Optical Vibration of Lamination Composite Optical Beams Using the Boubaker Polynomials Expansion Scheme and the Differential Quadrature Method

The effects of stacking sequences of composite laminated optical beams on free vibration frequencies are investigated using two methods: the Boubaker Polynomials Expansion Scheme (pbes) and the Differential Quadrature Method (dqm). In the last decades, these two techniques have been separately performed for obtaining accurate numerical solutions to several initial boundary value problems (Vo et al. 2010, Li et al. 2008, Chen 2003, Hu et al. 2008, Karami et al. 2003, Malekzadeh et al. 2004, Khare et al. 2004, Della and Shu 2005, Ramtekkar et al. 2002, Adam 2003). Conjointly yielded results are compared and discussed.

STRESS ANALYSIS OF A ROTATING FGM CIRCULAR DISC WITH EXPONENTIALLY-VARYING PROPERTIES

Hitit University Denizli,Turkey Corum, Turkey akursun@pau.edu.tr Muzaffer Topcu Pamukkale University Denizli, Turkey mtopcu@pau.edu.tr Ugur Yucel Pamukkale University Denizli, Turkey uyucel@pau.edu.tr ABSTRACT In this study, elastic stress analysis of a thin circular disc made of functionally graded materials (FGMs) subjected to a temperature load and an inertia force due to rotation of the disc is investigated. Based on the two dimensional thermoelastic theories, the axisymmetric problem is formulated in terms of a second order ordinary differential equation which is solved by finite difference method (FDM). The FGM disc is assumed to have exponential variation of material properties in radial direction only and Poisson’s ratio is kept constant. The result also compared with semi-analytical solution (SAS) and their consistence has been shown. Some numerical results of thermoelastic field are presented and discussed for an Al