Parametric Instability of Curved Girders
Publication: Journal of Structural Engineering
Volume 109, Issue 4
Abstract
The parametric instability of a curved girder subjected to equal and opposite periodic moments at the ends is examined. It is shown that the relationship of the frequencies at which parametric resonance occurs differs from the frequency relationship of ordinary resonance. For small values of the applied couples at the ends, the parametric resonant frequency is twice the natural frequency. The method presented can also be used to determine the natural frequencies and static buckling moment for a curved girder. Special analytical solutions and numerical results are obtained and presented in nondimensional forms.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bhattacharya, B., “Coupled Vibrations of Thin‐Walled Open Section Curved Beams,” Journal of Structural Engineering, Vol. 3, No. 1, 1975, pp. 29–35.
2.
Bjorhovde, R., “Research Needs in Stability of Metal Structures,” Journal of the Structural Division, ASCE, Vol. 106, No. ST12, Proc. Paper 15926, Dec., 1980, pp. 2425–2442.
3.
Bolotin, V. V., The Dynamic Stability of Elastic Systems, Holden‐Day, Inc., San Francisco, Calif., 1964.
4.
Christiano, P. P., and Culver, C. G., “Horizontally Curved Bridges Subject to Moving Load,” Journal of the Structural Division, ASCE, Vol. 95, No. ST8, Proc. Paper 6713, Aug., 1969, pp. 1615–1643.
5.
Chu, K. Y., “Beuluntersuchung von ebenen Stegblechen Kreisformig gekrummter Trager mit I‐Querschnitt,” Der Stahlbau, Vol. 35, No. 5, May, 1966, pp. 126–142.
6.
Culver, C. G., “Natural Frequencies of Horizontally Curved Beams,” Journal of the Structural Division, ASCE, Vol. 93, No. ST2, Proc. Paper 5187, Apr., 1967, pp. 189–203.
7.
Culver, C. G., and Frampton, R. E., “Local Instability of Horizontally Curved Members,” Journal of the Structural Division, ASCE, Vol. 96, No. ST2, Proc. Paper 7079, Feb., 1970, pp. 245–265.
8.
Fam, A. R. M., “Static and Free Vibration Analysis of Curved Box Bridges,” thesis presented to McGill University, at Montreal, Canada, in 1973, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
9.
Heins, C. P., and Sahin, M. A., “Natural Frequency of Curved Box Girders,” Journal of the Structural Division, ASCE, Vol. 105, No. ST12, Proc. Paper 15064, Dec., 1979, pp. 2591–2600.
10.
Komatsu, S., and Nakai, H., “Study on Free Vibration of Curved Girder Bridges,” Transactions, Japan Society of Civil Engineers, Tokyo, Japan, No. 136, Dec., 1966.
11.
Komatsu, S., and Nakai, H., “Fundamental Study on Forced Vibration of Curved Girder Bridges,” Japan Society of Civil Engineers, Tokyo, Japan, Vol. 2, Part I, 1970.
12.
McLachlan, N. W., Theory and Application of Mathieu Functions, Dover Publications, Inc., New York, N.Y., 1964.
13.
Ojalvo, I. U., and Newman, M., “Buckling of Naturally Curved and Twisted Beams,” Journal of the Engineering Mechanics Division, ASCE, Vol. 94, No. EMS, Oct., 1968, pp. 1067–1087.
14.
Ojalvo, M., Demuts, E., and Tokarz, F., “Out‐of‐Plane Buckling of Curved Elements,” Journal of the Structural Division, ASCE, Vol. 95, No. ST10, Oct., 1969, pp. 2305–2316.
15.
Rutenberg, A., “Vibration Properties of Curved Thin‐Walled Beams,” Journal of the Structural Division, ASCE, Vol. 105, No. ST7, Proc. Paper 14687, July, 1979, pp. 1445–1455.
16.
Shore, S., and Chaudhuri, S., “Free Vibration of Horizontally Curved Beams,” Journal of the Structural Division, ASCE, Vol. 98, No. ST3, Proc. Paper 8755, Mar., 1972, pp. 793–796.
17.
Tan, C. P., and Shore, S., “Dynamic Response of a Horizontally Curved Bridge,” Journal of the Structural Division, ASCE, Vol. 94, No. ST3, Proc. Paper 5862, Mar., 1968, pp. 761–781.
18.
Tan, C. P., and Shore, S., “Response of Horizontally Curved Bridge to Moving Load,” Journal of the Structural Division, ASCE, Vol. 94, No. ST9, Proc. Paper 6125, Sept., 1968, pp. 2135–2151.
19.
Timoshenko, S. P., and Gere, J. M., Theory of Elastic Stability, 2nd ed., McGraw‐Hill Book Co., Inc., New York, N.Y., 1961.
20.
Vlasov, V. Z., Thin Walled Elastic Beams, 2nd ed., National Science Foundation, Washington, D.C., 1961.
21.
Yoo, C. H., and Fehrenback, J. P., “Natural Frequencies of Curved Girders,” Journal of the Engineering Mechanics Division, ASCE, Vol. 107, No. EM2, Proc. Paper 16177, Apr., 1981, pp. 339–354.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 109 • Issue 4 • April 1983
Pages: 829 - 842
Copyright
Copyright © 1983 ASCE.
History
Published online: Apr 1, 1983
Published in print: Apr 1983
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.