On the Comparison of Timoshenko and Shear Models in Beam Dynamics
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of Engineering Mechanics
Volume 132, Issue 10
Abstract
The classical Timoshenko beam model and the shear beam model are often used to model shear building behavior both for stability or dynamic analysis. This technical note questions the theoretical relationship between both models for large values of bending to shear stiffness parameter. The simply supported beam is analytically studied for both models. Asymptotic solutions are obtained for large values of bending to shear stiffness parameter. In the general case, it is proven that the shear beam model cannot be deduced from the Timoshenko model, by considering large values of bending to shear stiffness parameter. This is only achieved for specific geometrical parameter in the present example. As a conclusion, the capability of the shear model to approximate Timoshenko model for large values of bending to shear stiffness parameter is firmly dependent on the material and geometrical characteristics of the beam section and on the boundary conditions.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abbas, B. A. H., and Thomas, J. (1977). “The secondary frequency spectrum of Timoshenko beams.” J. Sound Vib., 51(1), 123–137.
Aristizabal-Ochoa, J. D. (2004). “Timoshenko beam-column with generalized end conditions and nonclassical modes of vibration of shear beams.” J. Eng. Mech., 130(10), 1151–1159.
Boutin, C., and Hans, S. (2003). “Homogenization of periodic discrete medium: Application to dynamics of framed structures.” Comput. Geotech., 30, 303–320.
Bush, A. W. (1992). Perturbation methods for engineers and scientists, CRC Press, London.
Cheng, F. Y. (1970). “Vibrations of Timoshenko beams and frameworks.” J. Struct. Div. ASCE, ASCE, 96(3), 551–571.
Clough, R. W., and Penzien, J. (1975). Dynamics of structures, McGraw–Hill, New York.
Cowper, G. R. (1966). “The shear coefficients in Timoshenko’s beam theory.” J. Appl. Mech., 33, 335–340.
Geist, B., and McLaughlin, J. R. (1997). “Double eigenvalues for the uniform Timoshenko beam.” Appl. Math. Lett., 10(3), 129–134.
Huang, T. C. (1961). “The effect of rotary inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions.” J. Appl. Mech., 28, 579–584.
Karnovsky, I. A., and Lebed, O. I. (2001). Formulas for structural dynamics: Tables, graphs, and solutions, McGraw–Hill, New York.
Kausel, E. (2002). “Nonclassical modes of unrestrained shear beams.” J. Eng. Mech., 128(6), 663–667.
Timoshenko, S. P. (1921). “On the correction for shear of the differential equation for transverse vibrations of prismatic bars.” Philos. Mag., 41, 744–746.
Timoshenko, S. P. (1922). “On the transverse vibration of bars with uniform cross-section.” Philos. Mag., 43, 125–131.
Volovoi, V. V., Hodges, D. H., Berdichevsky, V. L., and Sutyrin, V. (1998). Dynamic dispersion curves for non-homogeneous, anisotropic beams with cross sections of arbitrary geometry, J. Sound Vib., 215(5), 1101–1120.
Yu, W., and Hodges, D. H. (2004). “Elasticity solutions versus asymptotic sectional analysis of homogeneous, isotropic, prismatic beams.” J. Appl. Mech., 71(1), 15–23.
Yu, W., and Hodges, D. H. (2005). “Generalized Timoshenko theory of the variational asymptotic beam sectional analysis.” J. Am. Helicopter Soc., 50(1), 46–55.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 10 • October 2006
Pages: 1141 - 1145
Copyright
© 2006 ASCE.
History
Received: Mar 17, 2005
Accepted: Jan 25, 2006
Published online: Oct 1, 2006
Published in print: Oct 2006
Notes
Note. Associate Editor: Hayder A. Rasheed
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.