Method for Improving Incomplete Modal Coupling
Publication: Journal of Engineering Mechanics
Volume 109, Issue 4
Abstract
The writers are concerned with the free vibration of discrete undamped linear dynamic systems commonly designed in structural engineering. The primary purpose is to present a rational method for improving the natural modes and frequencies computed by incomplete modal coupling, without increasing the order of the resultant eigenvalue problem. Improvement is accomplished through use of a candidate table in an iterative process that introduces significant modes into sequential modal analyses. The error trend and sensitivity analysis due to modal truncation is evaluated by computation of a scalar number called significance index which represents an approximation to the error in a certain eigenvalue due to omission of a certain mode shape. This information forms the basis of the candidate table, which serves as a guide for the optimal automated selection of modes for modal substitution. The method of analysis is demonstrated for a discrete model containing 378 degrees‐of‐freedom.
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References
1.
Bajan, R. L., and Feng, C. C., “Free Vibration Analysis by the Modal Substitution Method,” Proceedings, Second American Astronautical Society‐American Institute of Aeronautics and Astronautics Symposium, Denver, Colo., July 15–16, 1968.
2.
Bajan, R. L., Feng, C. C., and Jaszlics, I., “Vibration Analysis of Complex Structural Systems by Modal Substitution,” Proceedings of the 39th Shock and Vibration Bulletin, Monterey, Calif., Oct., 1968, pp. 99–105.
3.
Benfield, W. A., and Hruda, R. F., “Branch Modes Analysis of Vibrating Systems,” American Institute of Aeronautics and Astronautics Journal, Vol. 9, No. 7, July, 1971, pp. 1255–1261.
4.
Benfield, W. A., Bodley, C. S., and Morosow, G., “Modal Synthesis Methods,” Proceedings of the Symposium on Substructuring—Space Shuttle Dynamics and Aeroelasticity Working Group, Marshall Space Flight Center, Ala., Aug., 1972.
5.
Craig, R. R., and Bampton, M. C. C., “Coupling of Substructures for Dynamic Analysis,” American Institute of Aeronautics and Astronautics Journal, Vol. 6, No. 7, July, 1978, pp. 1313–1319.
6.
Gladwell, G. M. L., “Branch Mode Analysis of Vibrating Systems,” Journal of Sound and Vibration, Vol. 1, No. 1, Jan., 1964, pp. 41–59.
7.
Gladwell, G. M. L., “The Vibration of Frames,” Journal of Sound and Vibration, Vol. 1, Part 4, July, 1964, pp. 402–425.
8.
Goldman, R. L., “Vibration Analysis by Partitioning,” American Institute of Aeronautics and Astronautics Journal, Vol. 7, No. 6, June, 1969, pp. 1152–1154.
9.
Hart, G. C., Hurty, W. C., and Collins, J. D., “A Survey of Modal Synthesis Methods,” Proceedings, National Aeronautics and Space Engineering and Manufacturing Meeting, Los Angeles, Calif., Sept. 28–30, 1971.
10.
Hou, S. N., “Review of Modal Synthesis Techniques and a New Approach,” The Shock and Vibration Bulletin, Naval Research Laboratory, No. 40, Part 4, Washington, D.C., Dec., 1969, pp. 25–39.
11.
Hunn, B. A., “A Method of Calculating the Space Free Resonant Modes of an Aircraft,” Journal of the Royal Aeronautical Society, Vol. 57, London, England, June, 1953, pp. 420–422.
12.
Hunn, B. A., “A Method of Calculating the Normal Modes of an Aircraft,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 8, Part 1, 1955, pp. 38–58.
13.
Hurty, W. C., “A Criterion for Selecting Realistic Natural Modes of a Structure,” Technical Memorandum 33‐364, Jet Propulsion Laboratory, Pasadena, Calif., Nov., 1967.
14.
Hurty, W. C., “Dynamic Analysis of Structural Systems by Component‐Mode Synthesis,” Technical Report 32‐350, Jet Propulsion Laboratory, Pasadena, Calif., Jan., 1964.
15.
Hurty, W. C., “Dynamic Analysis of Structural Systems Using Component Modes,” American Institute of Aeronautics and Astronautics Journal, Vol. 3, No. 4, Apr., 1965, pp. 678–685.
16.
Hurty, W. C., “Introduction to Modal Synthesis Techniques,” Proceedings of the Synthesis of Vibrating Systems Conference, American Society of Mechanical Engineers, Washington, D.C., Nov. 30, 1971.
17.
Hurty, W. C., “Vibrations of Structural Systems by Component‐Mode Synthesis,” Journal of the Engineering Mechanics Division, ASCE, Vol. 86, No. EM4, Proc. Paper 2572, Aug., 1960, pp. 51–59.
18.
Hurty, W. C., and Rubinstein, M. F., “Dynamic Analysis of a Rocket and Model by the Component Modes Method,” Paper 925E, Society of Automative Engineers, New York, N.Y., Oct., 1964.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 109 • Issue 4 • August 1983
Pages: 937 - 949
Copyright
Copyright © 1983 ASCE.
History
Published online: Aug 1, 1983
Published in print: Aug 1983
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