Elastik Zemin Üzerinde Bulunan Bir Tarafı Ankastre Mesnetli Diğer Tarafı Serbest Homojen Olmayan Kirişin Serbest Titreşimi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2008Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2008Bu çalışmada elastik zeminin üzerinde bulunan bir tarafı ankastre diğer tarafı serbest homojen olmayan kirişin serbest titreşim problemi incelenmiştir. Önce, malzemenin yoğunluğu sabit, elastisite modülünün kalınlık koordinatına bağlı bileşeni sürekli ve uzunluk koordinatına bağlı bileşeni rastgele fonksiyonlar şeklinde seçilerek kirişin temel bağıntı ve titreşim denklemleri çıkarılmıştır. Sonra çökme fonksiyonları polinom şeklinde seçilerek titreşim frekansı için 3 değişik ifade elde edilmiştir. Sayısal hesaplarda, Monte Carlo yöntemi uygulanarak elastisite modülünün uzunluk bileşenine rastgele değerler verilerek doğal titreşim frekansı için bulunan her üç ifadede kalınlık koordinatına göre homojen durumda (veya homojen olmayan durumda) serbest titreşim frekansı değerlerinin deterministik ve eşit olduğu saptanmıştır. Kalınlık koordinatına göre homojen olmamanın serbest titreşim frekansına etkisi homojen duruma kıyasla önemli olduğu görülmüştür. Elastik zemin etkisi dikkate alındığında doğal frekansın değerleri zemin etkisinin dikkate alınmadığı durumlarla kıyaslandığında artmakta veyatak katsayısı değeri artığında bu etki daha da büyümekte olduğu görülmüştür. Literatürdeki sonuçlarla karsılaştırma yapılarak sonuçların doğruluğu saptanmıştır.Free vibrations of non-uniform beams with one end clamped the other end simply supported on an elastic foundation is investigated in this study. Firstly, assuming density of the material as constant and elasticity modulus of the beams are assumed to vary random according to the longitudinal direction and continuously according to 158 the thickness direction. Then, choosing the displacement functions as polynomials three different expressions for vibration frequency are obtained. In numerical computations, applying Monte Carlo method and taking random values for lengthiness constituent of elasticity modulus, it is seen that all three expressions of natural vibration frequency are deterministic and equal to the values for thickness constituent of elasticity modulus in homogeneous case (or non-homogeneous case). It is observed that the effects of non-homogeneity to the natural vibration frequency compared by homogeneity are very important. Also it is seen that natural frequency values are increased by considering the elastic foundation effect and compared with the conditions except elastic foundation effect, and the effect is more increased by increasing the “bedding” coefficient values. Comparisons were made with the values obtained in the literature to validate the results

Finite element modeling of contact between an elastic layer and two elastic quarter planes

WOS: 000579370800008In this study, a two dimensional model of receding contact problem has been analyzed using finite element method (FEM) based software ANSYS and ABAQUS. For this aim finite element modeling of elastic layer and two homogeneous, isotropic and symmetrical elastic quarter planes pressed by means of a rigid circular punch has been presented. Mass forces and friction are neglected in the solution. Since the problem is examined for the plane state, the thickness along the z-axis direction is taken as a unit. in order to check the accuracy of the present models, the obtained results are compared with the available results of the open literature as well as the results of two software are compared using Root Mean Square Error (RMSE) and good agreements are found. Numerical analyses are performed considering different values of the external load, rigid circular radius, quarter planes span length and material properties. the contact lengths and contact stresses of these values are examined, and their results are presented. Consequently, it is concluded that the considered non-dimensional quantities have noteworthy influence on the contact lengths and contact stress distributions, additionally if FEM analysis is used correctly, it can be an efficient alternative method to the analytical solutions that need time

Free Vibration of Functionally Graded Rayleigh Beam

In the present study the free vibration of Rayleigh beam composed of functionally graded materials (FGMs) is investigated. For this purpose, the equation of the motion of functionally graded (FG) beam derived according to Rayleigh beam theory. The material properties are assumed to vary continuously through the thickness of the beam according to the power-law form. Resulting equations are solved for simply supported boundary conditions. In order to validate the results, a comparisons is carried out with available results for homogeneous beam. The effects of varying material properties on the dimensionless free vibration frequency parameters are examined

Numerical Modelling of Wheel on the Snow

In the present study, a numerical model for wheel-snow interaction ispresented using finite element method. For this aim, the model of tire is designed using SolidWorks and ANSYS Design modeler. The analyses of the prepared models are performed using ANSYS Explicit Dynamics considering Mooney- Rivilin tire model. Frictional relationship between wheel and snow ground was established and snow erosion is considered as linear, in the analyses. To validate the results, a comparison is carried out with available results. Six different mesh sizes are considered in the study, the effect of mesh sizing and mesh number on the accuracy of the obtained results and solution time is discussed. Finally, it is concluded that models with 0.025 m and 0.02 m mesh sizes give more accurate results than the others and a strong linear proportion exists between the number of iteration and the mesh size

Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane

Avcar, Mehmet/0000-0002-0689-0601WOS: 000504404100008The present study deals with the numerical analysis of the symmetric contact problem of two bonded layers resting on an elastic half plane compressed with a rigid punch. in this context, Finite Element Method (FEM) based software called ANSYS and ABAQUS are used. It is assumed that the elastic layers have different elastic constants and heights and the external load is applied to the upper elastic layer by means of a rigid stamp. the problem is solved under the assumptions that the contact between two elastic layers, and between the rigid stamp are frictionless, the effect of gravity force is neglected. To validate the constructed model and obtained results a comparison is performed with the analytical results in literature. the numerical results for normal stresses and shear stresses are obtained for various parameters of load, material and geometry and are tabulated and illustrated.Recep Tayyip Erdogan University Scientific Research Project [FBA-2016-659]This research described in this paper was financially supported by the Recep Tayyip Erdogan University Scientific Research Project (Grant no: FBA-2016-659). the first and second authors would like to thank institution