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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:69845", author = "Faruk Fırat Çalım and Nurullah Karaca and Hakan Tacettin Türker", title = "Out-of-Plane Free Vibrations of Circular Rods", abstract = "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 = "Circular rod, Out-of-plane free vibration analysis,
Transfer Matrix Method.", volume = "9", number = "5", pages = "812-4", }