Vibration of Tapered Beams
Publication: Journal of Structural Engineering
Volume 111, Issue 1
Abstract
Stiffness and consistent mass matrices for linearly tapered beam element of any cross‐sectional shape are derived in explicit form. Exact expressions for the required displacement functions are used in the derivation of the matrices. Variation of area and moment of inertia of the cross section along the axis of the element is exactly represented by simple functions involving shape factors. Numerical results of vibration of some tapered beams are obtained using the derived matrices and compared with the analytical solutions and the solutions based upon stepped representation of the beams using uniform beam elements. The significance of the severity of taper within beams upon solution accuracy and convergence characteristics is examined.
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References
1.
Gere, J. M., and Carter, W. O., “Critical Buckling Loads for Tapered Columns,” Journal of the Structural Division, ASCE, Vol. 88, No. ST1, Paper 3045, Feb., 1962, pp. 1–11.
2.
Gupta, A. K., “Vibration Analysis of Linearly Tapered Beams Using Frequency‐Dependent Stiffness and Mass Matrices,” thesis presented to Utah State University, Logan, Utah, in 1975, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
3.
Heidebrecht, A. C., “Vibration of Non‐Uniform Simply‐Supported Beams,” Journal of the Engineering Mechanics Division, ASCE, Vol. 93, No. EM2, Apr., 1967, pp. 1–15.
4.
Wang, H. C., “Generalized Hypergeometric Function Solutions on the Transverse Vibration of a Class of Non‐Uniform Beams,” Journal of Applied Mechanics, Vol. 36, 1967, pp. 702–708.
Information & Authors
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Published In
Journal of Structural Engineering
Volume 111 • Issue 1 • January 1985
Pages: 19 - 36
Copyright
Copyright © 1985 ASCE.
History
Published online: Jan 1, 1985
Published in print: Jan 1985
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