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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 88
Edited by: B.H.V. Topping and M. Papadrakakis
Paper 308

The Out-Of-Plane Natural Frequencies of Curved Composite Beams Including the Effect of the Rotary Inertia and Shear Deformation

B. Ayhan and F. Kadioglu

Department of Civil Engineering, Istanbul Technical University, Turkey

Full Bibliographic Reference for this paper
B. Ayhan, F. Kadioglu, "The Out-Of-Plane Natural Frequencies of Curved Composite Beams Including the Effect of the Rotary Inertia and Shear Deformation", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 308, 2008. doi:10.4203/ccp.88.308
Keywords: free vibration, curved beam, dynamic analysis, finite element.

Curved beam structures have been widely used in many civil, mechanical and aerospace engineering applications such as spring design, curved girder bridges, tire dynamics, stiffeners in aircraft structures.

In this present study, an analysis for the out-of-plane vibration frequencies for different angles (0°, 45°, 60°, 90°) of fibers along the axis of a circular orthotropic beam will be given. The effect of shear deformation and rotary inertia are taken into account. The Gâteaux differential method (GDM) is employed to construct the functional and variational method [1] is applied to obtain the mixed finite element formulation [2]. The governing equations for out-of-plane scalar vibration can be found from the literature [3], in which, there are six variables including a shear force, a bending moment, a torsional moment, two components of rotation and a component of displacement. Field equations can be written in operator form and are given explicitly in matrix form of the operator. Therefore the functional corresponding to the field equations is obtained [2]. In dynamic analysis, the problem of the natural frequencies of free vibrating structural system reduces to the solution of the standard eigenvalue problem. To derive the finite element formulations, first the interpolation functions, by which all unknown internal quantities have been expressed, must be chosen and then are inserted into the functional. After extremization of this functional with respect to twelve nodal variables, the twelve element equations obtained are solved. A computer program is coded in FORTRAN to obtain the natural frequencies. The results are compared with those obtained using ANSYS.

All kinds of boundary conditions can be analyzed using the proposed method. This formulation can be used for wide and relatively thin structures due to the fact that this formulation is free from locking effects. Because of the properties of the new functional obtained by the GDM, it is possible to generate element matrices easily. An agreement is achieved as comparing the results obtained using ANSYS and the FORTRAN computer program.

J.D. Oden, J.N. Reddy, "Variational Method in Theoretical Mechanics", Springer, Berlin, 1976.
A.Y. Akoz, F. Kadioglu, "The mixed finite element solution of circular beam on elastic foundation", Computers & Structures, 60(4), 643-651, 1996. doi:10.1016/0045-7949(95)00418-1
V. Yildirim, "Common effects of the rotary inertia and shear deformation on the out-of-plane natural frequencies of composite circular bars", Composites: Part B, 32, 687-695, 2001. doi:10.1016/S1359-8368(01)00040-3

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