Mechanical Engineering / Makina Mühendisliği
Permanent URI for this collectionhttps://hdl.handle.net/11147/4129
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Article Citation - WoS: 15Citation - Scopus: 19Exact Longitudinal Vibration Characteristics of Rods With Variable Cross-Sections(Hindawi Publishing Corporation, 2011) Yardımoğlu, Bülent; Aydın, LeventLongitudinal natural vibration frequencies of rods (or bars) with variable cross-sections are obtained from the exact solutions of differential equation of motion based on transformation method. For the rods having cross-section variations as power of the sinusoidal functions of ax+b, the differential equation is reduced to associated Legendre equation by using the appropriate transformations. Frequency equations of rods with certain cross-section area variations are found from the general solution of this equation for different boundary conditions. The present solutions are benchmarked by the solutions available in the literature for the special case of present cross-sectional variations. Moreover, the effects of cross-sectional area variations of rods on natural characteristics are studied with numerical examples.Article Citation - WoS: 16Citation - Scopus: 19A Novel Finite Element Model for Vibration Analysis of Rotating Tapered Timoshenko Beam of Equal Strength(Elsevier Ltd., 2010) Yardımoğlu, BülentA new finite element model based on the coupled displacement field and the tapering functions of the beam is formulated for transverse vibrations of rotating Timoshenko beams of equal strength. In the coupled displacement field, the polynomial coefficients of transverse displacement and cross-sectional rotation are coupled through consideration of the differential equations of equilibrium. The tapering functions of breadth and depth of the beam are obtained from the principle of equal strength in the longitudinal direction of the beam. After finding the displacement functions using the tapering functions, the stiffness and mass matrices are expressed by using the strain and kinetic energy equations. A semi-symbolic computer program in Mathematica is developed and subsequently used to evaluate the new model. The results of the illustrative example regarding the problem indicated in the title of this paper are obtained and compared with the results found from the models created in ABAQUS. Very good agreement is found between the results of new model and the other results. © 2010 Elsevier B.V.Article Citation - WoS: 17Citation - Scopus: 22Vibration Analysis of Rotating Tapered Timoshenko Beams by a New Finite Element Model(Hindawi Publishing Corporation, 2006) Yardımoğlu, BülentA new finite element model is developed and subsequently used for transverse vibrations of tapered Timoshenko beams with rectangular cross-section. The displacement functions of the finite element are derived from the coupled displacement field (the polynomial coefficients of transverse displacement and cross-sectional rotation are coupled through consideration of the differential equations of equilibrium) approach by considering the tapering functions of breadth and depth of the beam. This procedure reduces the number of nodal variables. The new model can also be used for uniform beams. The stiffness and mass matrices of the finite element model are expressed by using the energy equations. To confirm the accuracy, efficiency, and versatility of the new model, a semi-symbolic computer program in MATLAB® is developed. As illustrative examples, the bending natural frequencies of non-rotating/rotating uniform and tapered Timoshenko beams are obtained and compared with previously published results and the results obtained from the finite element models of solids created in ABAQUS. Excellent agreement is found between the results of new finite element model and the other results.Article Citation - WoS: 11Citation - Scopus: 14Coupled Bending-Bending Vibration of a Rotating Pre-Twisted Beam With Aerofoil Cross-Section and Flexible Root by Finite Element Method(Hindawi Publishing Corporation, 2004) Yardımoğlu, Bülent; Inman, Daniel J.The purpose of this paper is to extend a previously published beam model of a turbine blade including the centrifugal force field and root flexibility effects on a finite element model and to demonstrate the performance, accuracy and efficiency of the extended model for computing the natural frequencies. Therefore, only the modifications due to rotation and elastic root are presented in great detail. Considering the shear center effect on the transverse displacements, the geometric stiffness matrix due to the centrifugal force is developed from the geometric strain energy expression based on the large deflections and the increase of torsional stiffness because of the axial stress. In this work, the root flexibility of the blade is idealized by a continuum model unlike the discrete model approach of a combination of translational and rotational elastic springs, as used by other researchers. The cross-section properties of the fir-tree root of the blade considered as an example are expressed by assigning proper order polynomial functions similar to cross-sectional properties of a tapered blade. The correctness of the present extended finite element model is confirmed by the experimental and calculated results available in the literature. Comparisons of the present model results with those in the literature indicate excellent agreement.Article Citation - WoS: 8Citation - Scopus: 6Coupled Bending-Bending Vibration of a Pre-Twisted Beam With Aerofoil Cross-Section by the Finite Element Method(Hindawi Publishing Corporation, 2003) Yardımoğlu, Bülent; Inman, Daniel J.The present study deals with a finite element model for coupled bending-bending-torsion vibration analysis of a pretwisted Timoshenko beam with varying aerofoil cross-section. The element derived in this paper has two nodes, with seven degrees of freedom at each node. The nodal variables are transverse displacements, cross-section rotations and the shear angles in two planes and torsional displacement. The advantage of the present element is the exclusion of unnecessary derivatives of fundamental nodal variables, which were included to obtain invertable square matrix by other researchers, by choosing proper displacement functions and using relationship between cross-sectional rotation and the shear deformation. Element stiffness and mass matrices are developed from strain and kinetic energy expressions by assigning proper order polynomial expressions for cross-section properties and considering higher order coupling coefficients. The correctness of the present model is confirmed by the experimental results available in the literature. Comparison of the proposed model results with those in the literature indicates that a faster convergence is obtained. The results presented also provide some insights in the formulation by clearly indicating that higher order coupling terms have considerable influence on the natural frequencies.