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Out-of-Plane Free Vibrations of Circular Rods

Authors: Faruk Fırat Çalım, Nurullah Karaca, Hakan Tacettin Türker


In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: transfer matrix method, circular rod, out-of-plane free vibration analysis

Digital Object Identifier (DOI):

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[1] V. Haktanır, and E. Kıral, “Statical Analysis of Elastically and Continuously Supported Helicoidal Structures by the Transfer and Stiffness Matrix Methods,” Computers & Structures, 49(4), 663-77, 1993.
[2] V. Haktanır, and E. Kıral, “Determination of free vibration of helical spring under prescribed initial conditions by the mod-superposition technique,” Journal of Çukurova University Faculty of Engineering and Architecture 1(5), 1990. (in Turkish)
[3] V. Haktanır, “Investigation of static, dynamic and buckling behavior of the helical systems by the transfer and stiffness matrix methods,” Ph.D. thesis, Çukurova University, Department of Mechanical Engineering, 1990.(in Turkish)
[4] B. K. Lee, S. J. Oh, J. M. Mo, and T. E. Lee, “Out-of-plane free vibrations of curved beams with variable curvature,” Journal of Sound and Vibration, 318, pp. 227-246, 2008.
[5] Y. O. Doğruer, and E. Tüfekçi, “Out-of-plane free vibration of a circular arch with uniform cross-section,” Journal of Engineering and Technical University of Istanbul, 6(2), 53-62, 2007. (in Turkish)
[6] E. Tüfekçi, and Y. O. Doğruer, “Out-of-plane free vibration of a circular arch with uniform cross-section: Exact solution,” Journal of Sound and Vibration, 291, 525-538, 2006.
[7] Z. Fang, “Dynamic Analysis of Structures with Uncertain Parameters Using the Transfer Matrix Method,” Computers & Structures, 55(6), pp. 1037-1044, 1995.
[8] K. Kang, C. W. Bert, and A. G. Stritz, “Vibration analysis of shear deformable circular arches by the differential quadrature method,” Journal of Sound and Vibration, 181, pp. 353-360, 1995.
[9] W. P. Howson, and A. K. Jemah, “Exact out-of-plane natural frequencies of curved Timoshenko beams,” Journal of Engineering Mechanics, 125, pp. 19-25, 1999.
[10] T. Irie, G. Yamada, and K. J. Tanaka, “Natural frequencies of in-plane vibration of arcs,” Journal of Applied Mechanics, ASME, Des. Data Meth. 50, pp. 449-452, 1983.
[11] M. İnan, “Transfer Matrix Methods in Elastomechanics,” Technical University of Istanbul, Faculty of Civil Engineering, No.585, 1964.(in Turkish)
[12] M. İnan, “General Theory of Elastic Bars. İ.T.U. Publications”, No 642, İstanul, 1969.(in Turkish)
[13] B. Tabarrok, A. N. Sinclair, M. Farshad, and H. Yi, “On the dynamics of spatially curved and twisted rods-a finite element formulation,” Journal of Sound and Vibration, 123, pp. 315-326, 1988.
[14] V. Yıldırım, “Free vibration analysis of helical spring with the stiffness matrix method,” Journal of Turkish Engineering and Environment, 19/4, 343-356, 1995. (in Turkish)
[15] V. Yıldırım, “A computer program for the free vibration analysis of elastic arcs,” Computers & Structures, 3(62), pp. 475-485, 1997.