Improved Time‐History Analysis for Structural Dynamics. II: Reduction of Effective Number of Degrees of Freedom
This article is a reply.
VIEW THE ORIGINAL ARTICLEPublication: Journal of Engineering Mechanics
Volume 119, Issue 12
Abstract
A crude analysis of a dynamic system involves very few degrees of freedom. When a more refined model is desired, more degrees of freedom must be introduced. This will increase the number of modes present and result in modes with very high frequencies in the model. The presence of these modes causes severe restriction in the size of time interval that can be used for step‐by‐step dynamic analysis in nonlinear problems. This restriction is removed by a new type of perturbation procedure that generalizes the method of static condensation and can treat relaxation of constraints in addition to variables associated with small masses. The additional degrees of freedom are treated algebraically rather than as true dynamic variables. The method is applied to structures with significant material nonlinearity. The lower‐frequency motions are corrected as a result of the presence of the additional degrees of freedom, but the very high frequency motions are not introduced. Thus, the time interval is selected corresponding to the highest frequency involving only the dynamic variables rather than to the much higher freqencies that would ordinarily be present.
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References
1.
Bathe, K. J., and Cimento, A. P. (1980). “Some practical procedures for the solution of nonlinear finite element equations.” J. Computer Methods in Appl. Mech. and Engrg., 22(1), 59–85.
2.
Bathe, K. J., and Gracewski, S. (1981). “On nonlinear dynamics analysis using substructuring and mode superposition.” Comput. Struct., 13(5–6), 699–707.
3.
Chen, C.‐C., and Robinson, A. R. (1993). “Improved time‐history analysis for structural dynamics calculations I: treatment of rapidly varying excitation and material nonlinearity.” J. Engrg. Mech., 119(12), 2496–2513.
4.
Collatz, L. (1966). The numerical treatment of differential equations. Springer‐Verlag, New York, N.Y.
5.
Dekker, K., and Verwer, J. G. (1984). Stability of Runge‐Kutta methods for stiff nonlinear differential equations. Elsevier Science Publishing Company, Inc., New York, N.Y.
6.
Geschwindner, L. F. (1981). “Nonlinear dynamic analysis by modal superposition.” J. Struct. Div., ASCE, 107(12), 2324–2336.
7.
Houbolt, J. C. (1950). “A recurrence matrix solution for the dynamic response of elastic aircraft.” J. Aeronautical Sci., 17(9), 540–550.
8.
Hughes, T. (1987). The finite element method. Prentice‐Hall, Inc., Englewood Cliffs, N.J., 515–517.
9.
Idelsohn, S. R., and Cardona, A. (1985). “A reduction method for nonlinear structural dynamic analysis.” J. Computer Methods in Appl. Mech. and Engrg., 49(3), 253–279.
10.
Knight, N. F. Jr. (1985). “Nonlinear structural dynamic analysis using a modified modal method.” AIAA J., 23(10), 1594–1601.
11.
Mohraz, B., Elghadamsi, F. E., and Chang, C.‐J. (1991). “An incremental mode superposition for non‐linear dynamic analysis.” Int. J. Earthquake Engrg. and Struct. Dynamics, 20(5), 471–481.
12.
Morris, N. F. (1977). “The use of modal superposition in nonlinear dynamics.” Comput. Struct., 7(1), 65–72.
13.
Moulton, F. R. (1914). An introduction to celestial mechanics. 2d Ed., Macmillan Co., New York, N.Y., 366–431.
14.
Newmark, N. M. (1959). “A method of computation for structural dynamics.” J. Engrg. Mech. Div., ASCE, 85(3), 67–94.
15.
Noor, A. K. (1981). “Recent advances in reduction methods for nonlinear problems.” Comput. Struct., 13(1–3), 31–44.
16.
Remseth, S. N. (1979). “Nonlinear static and dynamic analysis of framed structures.” Comput. Struct., 10(6), 879–897.
17.
Santana, G., and Robinson, A. R. (1986). Dynamic analysis of modified structural systems, Civil Engineering Studies, Structural Research Series No. 525, University of Illinois at Urbana, Urbana, Ill.
18.
Shah, V. N., Bohm, G. J., and Nahavandi, A. N. (1979). “Modal superposition method for computationally economical nonlinear structural analysis.” J. Pressure Vessel Technol. Trans. ASME, 101(2), 134–141.
19.
Wilson, E. L., Farhoomand, I., and Bathe, K. J. (1973). “Nonlinear dynamics analysis of complex structures.” Int. J. Earthquake Engrg. and Struct. Dynamics, 1(3), 241–252.
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Copyright © 1993 American Society of Civil Engineers.
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Received: May 26, 1992
Published online: Dec 1, 1993
Published in print: Dec 1993
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