Dynamic Response of Beams on Elastic Foundation
Publication: Journal of Structural Engineering
Volume 118, Issue 3
Abstract
A method is proposed for dynamic analysis of beams on an elastic foundation. The method develops mass and stiffness matrices of a beam on an elastic foundation finite element from the exact solution of the shape functions governing its end deformations. The developed matrices can be combined with conventional beam element matrices to obtain assembled matrices, which can be used to determine natural frequencies and mode shapes of a general structure. Since the proposed method is based on the exact solution of the related differential equation, the accuracy is independent of element refinement. This is in contrast to other methods in which the accuracy is dependent on the number of elements modeled due to approximate modeling of the elastic foundation as discrete soil springs. The proposed method can be further expanded for forced vibration problems, such as earthquake problems, to determine dynamic response under time varying loads. Numerical examples are presented to demonstrate the effectiveness of the proposed method.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bowles, J.E. (1974). Analytical and computer methods in foundation engineering.McGraw‐Hill, Inc., New York, N.Y.
2.
Bowles, J. E. (1977). Foundation analysis and design. 2 Ed., McGraw‐Hill, Inc., New York, N.Y.
3.
James, M. L., Smith, G. M., Wolford, J. C., and Whaley, P. W. (1989). Vibration of mechanical and structural systems. Harper & Row, Publishers, Inc., New York, N.Y.
4.
Lai, Y. C. (1990). “Dynamic response of beams on elastic foundation,” thesis presented to the University of Missouri at Kansas City, at Independence, Mo. In partial fulfillment of the requirements for the degree of Master of Science.
5.
Miranda, C., and Nair, K. (1966). “Finite beams on elastic foundation.” J. Struct. Div., 92(2), 131–142.
6.
Popov, E. P. (1976). Mechanics of materials. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
7.
Timoshenko, S., and Young, D. H. (1964). Vibration problems in engineering. Van Nostrand Reinhold, New York, N.Y.
8.
Ting, B. Y., and Mockry, E. F. (1984). “Beam on elastic foundation finite element.” J. Struct. Engrg., 110(10), 2324–2339.
Information & Authors
Information
Published In
Copyright
Copyright © 1990 ASCE.
History
Published online: Mar 1, 1992
Published in print: Mar 1992
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.