Mechanical Engineering / Makina Mühendisliği

Permanent URI for this collectionhttps://hdl.handle.net/11147/4129

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Author: search.filters.author.Yardımoğlu, BülentSubject: search.filters.subject.Finite element method

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 16
    Citation - Scopus: 19
    A Novel Finite Element Model for Vibration Analysis of Rotating Tapered Timoshenko Beam of Equal Strength
    (Elsevier Ltd., 2010) Yardımoğlu, Bülent
    A 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: 39
    Citation - Scopus: 46
    Finite Element Model for Vibration Analysis of Pre-Twisted Timoshenko Beam
    (Academic Press Inc., 2004) Yardımoğlu, Bülent; Yıldırım, Tolga
    A new linearly pre-twisted Timoshenko beam finite element, which has two nodes and four-degrees-of-freedom per node, is developed and subsequently used for coupled bending-bending vibration analysis of pre-twisted beams with uniform rectangular cross-section. First, displacement functions based on two coupled displacement fields (the polynomial coefficients are coupled through consideration of the differential equations of equilibrium) are derived for pre-twisted beams whose flexural displacements are coupled in two planes. This approach helps to reduce the number of nodal variables. Next, the stiffness and mass matrices of the finite element model are obtained by using the energy expressions. Finally, the natural frequencies of pre-twisted Timoshenko beams are obtained and compared with previously published theoretical and experimental results to confirm the accuracy and efficiency of the present model. Excellent agreement is found with the previous studies. Also, the new pre-twisted Timoshenko beam element has good convergence characteristics.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 6
    Coupled 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.