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http://dx.doi.org/10.5050/KSNVE.2012.22.3.223

Free Vibrations of Timoshenko Beam with Constant Volume  

Lee, Byoung-Koo (원광대학교 토목환경공학과)
Lee, Tae-Eun (원광대학교 토목환경공학과)
Yoon, Hee-Min (원광대학교 대학원 토목환경공학과)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.22, no.3, 2012 , pp. 223-233 More about this Journal
Abstract
This paper deals with free vibrations of the tapered Timoshenko beam with constant volume, in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the regular polygon cross section whose depth is varied with the parabolic function. The ordinary differential equations governing free vibrations of such beam are derived based on the Timoshenko beam theory by decomposing the displacements. Governing equations are solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.
Keywords
Free Vibration; Constant Volume; Tapered Beam; Timoshenko Beam; Rotatory Inertia; Shear Deformation; Mode Shape; Natural Frequency;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 Li, J., Li, X. and Hua, H., 2009, Free Vibration Analysis of Third-order Shear Deformable Composite Beams using Dynamic Stiffness Method.Archive of Applied Mechanics, Vol. 79, pp. 1083-1098.   DOI
2 Timoshenko, S. P., Young, D. H. and Weaver, W., 1974, Vibration Problems in Engineering, Wiley, USA.
3 Carnahan, B., Luther, H. A. and Wilkes, J. O., 1969, Applied Numerical Methods, John Wiley and Sons, USA.
4 Lee, T. E. and Lee, B. K., 2011, Free Vibration Analysis of Parabolic Hollowed Beamcolumns with Constant Volume, Transactions of the Korea Society for Noise and Vibration Engineering, Vol. 21, No. 4, pp. 384-391.   DOI
5 Lee, B. K., Oh, S. J., Mo, J. M. and Lee, T. E., 2008, Out-of-plane Free Vibrations of Curved Beams with Variable Curvature, Journal of Sound and Vibration, Vol. 318, pp. 227-246.   DOI
6 Lee, B. K., Lee, T. E. and Choi, J. M., 2011, Dynamic Optimal Arches with Constant Volume, International Journal of Structural Stability and Dynamics, Accepted for Publication in September, 2011.
7 Takahashi, I., 1999, Vibration and Stability of Non-uniform Cracked Timoshenko Beam Subjected to Follower Force, Computers & Structures, Vol. 71, pp. 585-591.   DOI
8 Yardimoglu, B. and Yildrim, T., 2004, Finite Element Model for Vibration Analysis of Pre-twisted Timoshenko Beam, Journal of Sound and Vibration, Vol. 273, pp. 741-754.   DOI
9 Zhou, D., 2000, Free Vibration of Multi-span Timoshenko Beams using Static Timoshenko Beam Functions, Journal of Sound and Vibration, Vol. 241, No. 4, pp. 725-734.   DOI
10 Zhong, H. and Guo, Q., 2003, Nonlinear Vibration of Timoshenko Beams using the Differential Quadrature Method, Nonlinear Dynamics, Vol. 32, pp. 223-234.   DOI
11 Lee, B. K., Oh, S. J., Jin, T. K. and Lee, J. K., 1999, Coupled Flexural-torsional Vibrations of Timoshenko Beams of Monosymmetric Cross-section Including Warping, Transactions of the Korea Society for Noise and Vibration Engineering, Vol. 9, No. 5, pp. 1012-1018.
12 Ho, S. H. and Chen, C. K., 2006, Free Transverse Vibration of an Axially Loaded Nonuniform Spinning Twisted Timoshenko Beam using Differential Transform, International Journal of Mechanical Sciences. Vol. 48, pp. 1323-1331.   DOI
13 Prokić, A., 2006, On Fivefold Coupled Vibrations of Timoshenko Thin-walled Beams. Engineering Structures, Vol. 28, pp. 54-62.   DOI   ScienceOn
14 Kaya, M. O. and Ozgumus, O. O., 2007, Flexural-torsional-coupled Vibration Analysis of Axially Loaded Closed-section Composite Timoshenko Beam by using DTM, Journal of Sound and Vibration, Vol. 306, pp. 495-506.   DOI
15 Sapountzakis, E. J. and Dourakopoulos, J. A., 2009, Nonlinear Dynamics Analysis of Timoshenko Beam by BEM, Nonlinear Dynamics, Vol. 58, pp. 307-318.   DOI