Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Conference Object Citation - Scopus: 6Coupled Out of Plane Vibrations of Spiral Beams(American Institute of Aeronautics and Astronautics Inc. (AIAA), 2009) Karami, M. A.; Yardımoğlu, Bülent; Inman, Daniel J.An analytical method is proposed to calculate the natural frequencies and corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equation and the boundary conditions are derived using Hamilton's principle. The vibration problem of a constant radius curved beam is solved using a general exponential solution with complex coefficients. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the R′ terms have negligible effect on the structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joint together to consider the slow change of radius along the spiral. The natural frequencies and mode shapes of two spiral structures have been calculated for illustration.Article Citation - WoS: 31Citation - Scopus: 34Vector Shock Soliton and the Hirota Bilinear Method(Elsevier Ltd., 2005) Pashaev, Oktay; Tanoğlu, GamzeThe Hirota bilinear method is applied to find an exact shock soliton solution of the system reaction-diffusion equations for n-component vector order parameter, with the reaction part in form of the third order polynomial, determined by three distinct constant vectors. The bilinear representation is derived by extracting one of the vector roots (unstable in general), which allows us reduce the cubic nonlinearity to a quadratic one. The vector shock soliton solution, implementing transition between other two roots, as a fixed points of the potential from continuum set of the values, is constructed in a simple way. In our approach, the velocity of soliton is fixed by truncating the Hirota perturbation expansion and it is found in terms of all three roots. Shock solitons for extensions of the model, by including the second order time derivative term and the nonlinear transport term are derived. Numerical solutions illustrating generation of solitary wave from initial step function, depending of the polynomial roots are given.Article Citation - WoS: 43Citation - Scopus: 43Shock Waves, Chiral Solitons and Semiclassical Limit of One-Dimensional Anyons(Elsevier Ltd., 2004) Lee, Jyh Hao; Lin, Chi-Kun; Pashaev, OktayThis paper is devoted to the semiclassical limit of the one-dimensional Schrödinger equation with current nonlinearity and Sobolev regularity, before shocks appear in the limit system. In this limit, the modified Euler equations are recovered. The strictly hyperbolicity and genuine nonlinearity are proved for the limit system wherever the Riemann invariants remain distinct. The dispersionless equation and its deformation which is the quantum potential perturbation of JNLS equation are also derived.Article Citation - WoS: 29Citation - Scopus: 33Areally-Averaged Overland Flow Equations at Hillslope Scale(Taylor and Francis Ltd., 1998) Tayfur, Gökmen; Kavvas, M. LeventMicroscale-averaged inter-rill area sheet flow and rill flow equations (Tayfur and Kavvas, 1994) are averaged along the inter-rill area length and rill length to obtain local areally-averaged inter-rill area sheet flow and rill flow equations (local-scale areal averaging). In this averaging, the local areally-averaged flow depths are related to the microscale-averaged flow depths at the outlet sections (downstream ends) of a rill and an inter-rill area by the assumption that the flow in these sections has the profile of a sine function. The resulting local areally-averaged flow equations become time dependent only. To minimize computational efforts and economize on the number of model parameters, local areally-averaged flow equations are then averaged over a whole hillslope section (hillslope-scale areal averaging). The expectations of the terms containing more than one variable are obtained by the method of regular perturbation. Comparison of model results with observed data is satisfactory. The comparison of the model results with those of previously developed models which use point-scale and large-scale (transectionally) averaged technology indicates the superiority of this model over them. Microscale-averaged inter-rill area sheet flow and rill flow equations (Tayfur & Kavvas, 1994) are averaged along the inter-rill area length and rill length to obtain local areally-averaged inter-rill area sheet flow and rill flow equations (local-scale areal averaging). In this averaging, the local areally-averaged flow depths are related to the microscale-averaged flow depths at the outlet sections (downstream ends) of a rill and an inter-rill area by the assumption that the flow in these sections has the profile of a sine function. The resulting local areally-averaged flow equations become time dependent only. To minimize computational efforts and economize on the number of model parameters, local areally-averaged flow equations are then averaged over a whole hillslope section (hillslope-scale areal averaging). The expectations of the terms containing more than one variable are obtained by the method of regular perturbation. Comparison of model results with observed data is satisfactory. The comparison of the model results with those of previously developed models which use point-scale and large-scale (transectionally) averaged technology indicates the superiority of this model over them