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Öğe Çatlak İçeren Silindirik Borularda SH Dalgası Yayılımı(2017) Kara, Hasan FaikBu çalışmada, sonsuz ortamda gömülü ve içten dışa dogru düzgün bir çatlak içeren silindirik boruların SH dalgaları etkisi altındaki davranışı incelenmiştir. Ele alınan dalga yayılımı probleminde, silindirik borunun düzgün bir çatlak içermesi, yapılan çalışmayı literatürdeki mevcut çalışmalardan ayırmaktadır. Boru ve sonsuz ortamın homogen, izotrop ve lineer elastik davranış gösterdigi ve çatlak yüzeyinde sürtünme olmadığı varsayılmıştır. Çözümde analitik ve sayısal yöntemler birlikte kullanılmıştır. Boru içerisinde ve sonsuz ortamdaki yer degiştirme fonksiyonları, dalga fonksiyonları açılımı tekniği ile kapalı formda Bessel fonksiyon serileri olarak elde edilmiştir. Elde edilen çözüm serileri, Sommerfeld Radyasyon Koşulunu ve boru iç yüzeyindeki sıfır gerilme şartını tam olarak saglar. Bu iki koşuldan, Bessel fonksiyon serilerindeki bilinmeyen kompleks katsayıların bir bölümü elde edilmiştir. Kalan katsayılar, boru ve sonsuz ortam arasındaki sınır koşullarının En Küçük Kareler Yöntemi ile yaklaşık olarak saglatılması ile bulunmuştur. Elde edilen sonuçlar, çatlaksız boruya ait kesit çözümler ile kıyaslanmıştır ve çatlagın gerilmeler üzerine etkisi grafiklerle gösterilmiştir.Öğe Diffraction of Plane SH Waves by a Cylindrical Cavity in an Infinite Wedge(Elsevier Science Bv, 2016) Kara, Hasan FaikDiffraction of plane harmonic SH waves by a cylindrical cavity in a homogeneous, isotropic and linear elastic infinite wedge is investigated. Analytical closed form solution is obtained by utilizing Wave Function Expansion Method and Image Technique. Governing equation of this two dimensional steady-state wave motion problem is the Helmholtz equation. Helmholtz equation for polar coordinates is solved by using Separation of Variables Method. Displacement fields are expressed in terms of Fourier Bessel series in complex form. Complex coefficients of Fourier-Bessel series are to be determined from boundary conditions. Zero-stress boundary condition at cavity inner surface is satisfied directly since polar coordinate systems are used. Free stress conditions at flat surfaces of the infinite wedge are satisfied in closed form via imaging method. In this technique, imaginary cavities symmetric with respect to flat surfaces are considered. With this consideration, scattered waves from imaginary cavities would represent reflections from flat surfaces so that stress free boundary condition on flat surfaces would be automatically satisfied. This technique would generate two additional displacement fields with two additional set of unknown complex Fourier-Bessel constants. These unknowns could be determined from boundary conditions of imaginary cavities. The cylindrical scattered waves from each cavity are defined in different polar coordinate systems. Addition Theorems are used for adequate coordinate transformation. Since Image Technique is used, to maintain angular symmetry, analytical solutions are obtained for a specific wedge whose internal angle is 120 degrees. Also, direction of incident waves has to be either horizontal or on the symmetry line of the wedge and cavity center has to be on the symmetry line. In numerical results, parameters in length dimension are normalized with respect to cavity radius. (C) 2016 The Authors. Published by Elsevier LtdÖğe Dynamic response of a functionally graded tube embedded in an elastic medium due to SH-Waves(Elsevier, 2018) Kara, Hasan Faik; Aydogdu, MetinDynamic response of a cylindrical tube surrounded by an unbounded elastic medium due to plane harmonic SH-Waves is studied. A two-dimensional mathematical model is considered. Cylindrical coordinates are used for convenience. The surrounding medium is assumed to be homogeneous, isotropic and linear elastic. The tube is assumed to be made of linear elastic functionally graded materials (FGMs) such that shear modulus and shear wave velocity are assumed to change linearly from inner surface to outer surface. Material properties are constant along circumferential direction. It is assumed that the inner surface of the tube is traction-free and there is a welded contact between the tube and the surrounding medium. Governing equations are slightly different in the tube region and the unbounded region. Both of the governing equations are solved by applying Finite Fourier Transform in circumferential direction. The exact solution series are presented in terms of Fourier-Bessel series in the unbounded region and power series in the tube region. The presented numerical results show that when the incoming wave lengths decrease, shear stresses at the tube increase significantly. It was shown that for the shorter incoming wave lengths, tubes made of FGMs are subjected to smaller shear stresses compared to the tubes homogeneously made of outer surface material of the FG cases.Öğe Dynamic response of an alluvial valley consists of three types of soil(Springer, 2020) Kara, Hasan FaikDynamic response of an alluvial valley consisting of three different types of soil was studied. In the two-dimensional model, the alluvial valley was assumed to have half-cylindrical shape. The alluvial valley contained three different types of soil with different shapes. The valley was surrounded by a half-space. All of the soil types and the half-space were assumed to be isotropic, homogeneous and linear elastic. The half-space was excited by simple harmonic SH-waves radiated from a strike-slip fault. The fault was assumed to have circular-arc shape in the mathematical model. The governing equations were solved by using wave function expansion method where boundary conditions were relatively simple. In the regions where boundary conditions were more complex, finite difference method was employed. Consequently, the wave propagation problem was solved semi-analytically. The obtained numerical results showed that surface displacement amplitudes are significantly affected by the material properties of the different soil types of the alluvial valley. It was also observed that the shapes of the soil types in the alluvial valley played a considerable role in surface displacements.Öğe A note on response of tunnels to incident SH-waves near hillsides(Elsevier Sci Ltd, 2016) Kara, Hasan FaikIn this study, diffraction of plane SH waves by a cylindrical tunnel embedded in homogeneous, isotropic and linear elastic quarter-space is investigated. Analytical solution techniques are used to solve the two dimensional wave propagation problem. When the excitation is assumed to be harmonic, the governing equation would be the Helmholtz equation. By applying separation of variables method to Helmholtz equation for cylindrical coordinates, general solutions are obtained in terms of Fourier-Bessel series. Unknown complex constants of the Fourier-Bessel series are to be determined from boundary conditions. Boundary conditions at inner and outer side of the tunnel are satisfied directly since they are defined in cylindrical coordinates. Stress-free boundary conditions at the ground and the hillside surfaces are satisfied in closed form via imaging method and addition theorems. Numerical examples are compared with earlier studies and the effect of the tunnel is discussed. (C) 2016 Elsevier Ltd. All rights reserved.
