Dynamic Stability Analysis by Matrix Function
Publication: Journal of Engineering Mechanics
Volume 113, Issue 7
Abstract
The matrix function method is applied to the dynamic stability problems of initially imperfected columns and plates under time‐dependent axial compression in elastic and elastic‐plastic regions. Matrix functions are derived from the solution of ordinary differential equation systems in a manner similar to that for scalar equations. The rigid body spring mode (RBSM) is adopted for presenting the spatial properties of the structural members. In this model, each element consists of rigid bodies with a rotational spring, which allows the restoring forces to be taken into consideration. In the numerical examples in the elastic and elastic‐plastic regions, the propoosed method, based on the reanalysis technique, is compared with other methods based on the incremental procedure. It is concluded that the proposed method is numerically efficient, general, and practical for the dynamic stability analysis of structural systems.
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References
1.
Anderson, T. L., and Moody, M. L., “Parametric Vibration Response of Columns,” Journal of the Engineering Mechanics Division, ASCE, Vol. 95, No. 3, Jun., 1969, pp. 665–677.
2.
Bolotin, V. V., The Dynamic Stability of Elastic Systems, translated by V. I. Weingarten, et al., Holden‐Day, trans., San Francisco, Calif., 1964.
3.
Cheng, F. Y., and Oster, B. K., “Ultimate Instability of Earthquake Structures,” Journal of the Structural Division, ASCE, Vol. 102, No. 5, May, 1976, pp. 961–972.
4.
Duffield, R. C., and Willems, N., “Parametric Resonance of Stiffened Rectangular Plates,” Journal of Applied Mechanics, ASME, Vol. 39, Mar., 1972, pp. 217–226.
5.
Friedmann, P., and Hammond, C. E., “Efficient Numerical Treatment of Periodic Systems with Application to Stability Problems,” International Journal for Numerical Methods in Engineering, Vol. 11, 1977, pp. 1117–1136.
6.
Grundmann, H., “Der Einfluß der Baustoffdämpfung auf das Stabilitätsproblem des gelenkig gelagerten Stabes unter pulsierender Axiallast,” Der StahlbauVol. 45, No. 2, 1976, pp. 46–54 (in German).
7.
Hara, T., Shigematsu, T., and Ohga, M., “Numerische Berechnung bei nichtelastischen Schwingungssystemen mit Hilfe von Matrizenfunktionen,” Bauingenieur, Vol. 60, No. 2, 1985, pp. 53–58 (in German).
8.
Hsu, C. S., “On the Parametric Excitation of a Dynamic System Having Multiple Degrees of Freedom,” Journal of Applied Mechanics, ASME, Vol. 30, No. 9, 1963, pp. 367–372.
9.
Hutt, J. M., and Salam, A. E., “Dynamic Stability of Plates by Finite Element,” Journal of the Engineering Mechanic Division, ASCE, Vol. 97, No. 3, Jun., 1971, pp. 879–899.
10.
Jasbier, S. A., “Survey of Structural Reanalysis Techniques,” Journal of the Structural Division, ASCE, Vol. 102, No. 4, Apr., 1976, pp. 783–802.
11.
Kawai, T., and Kondou, K., “New Beam and Plate Bending Elements in Finite Element Analysis,” Seisan Kenkyu, Vol. 28, No. 9, 1976, pp. 409–412.
12.
Krings, W., and Waller, H., “Berechnung von Instationären Tragwerkssch‐wingungen mit Hilfe von Matrizenfunktionen,” Die Bautechnik, Vol. 51, No. 1, 1974, pp. 8–12 (in German).
13.
Krings, W., and Waller, H., “Numerische Berechnung von Gedämpften Schwingungssystemen bei Nichtperiodischen Erregungen,” Die Bautechnik, Vol. 52, No. 3, 1975, pp. 97–103 (in German).
14.
Newmark, N. M., “A Method of Computation for Structural Dynamics,” Journal of the Engineering Mechanics Division, ASCE, Vol. 85, No. 3, Jul., 1959, pp. 67–94.
15.
Shigematsu, T., Hara, T., and Ohga, M., “Zur Numerischen und Experimentellen Schwingungsuntersuchung von Bauwerken unter Unregelmäßiger Belastung,” Bauingenieur, Vol. 59, No. 3, 1984, pp. 97–101 (in German).
16.
Shigematsu, T., Hara, T., and Ohga, M., “Dynamische Stabilität des Vorverformten Stabes unter Pulsierender Axialbelastung,” Bautechnik, Vol. 63, No. 2, 1986, pp. 57–62 (in German).
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Published In
Journal of Engineering Mechanics
Volume 113 • Issue 7 • July 1987
Pages: 1085 - 1100
Copyright
Copyright © 1987 ASCE.
History
Published online: Jul 1, 1987
Published in print: Jul 1987
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