Dynamics of Frames With Axial Constraints
Publication: Journal of Structural Engineering
Volume 109, Issue 3
Abstract
The number of degrees of freedom for the dynamic analysis of plane and space frames may be considerably reduced by introducing axial constraints. Determination of the rank and basis of the constraint matrix by Gauss‐Jordan elimination with pivoting leads to automatic selection of the best set of dependent and independent joint translations. Then a transformation of the equations of motion to generalized coordinates produces a reduced set of equations that may be solved for the dynamic response of the independent joint translations. This technique can be applied in conjunction with the elimination of joint rotations, thereby accomplishing a double reduction without significant loss of accuracy. The procedure described has been programmed on a digital computer for both plane and space frames, with automatic identification of redundant constraints.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Archer, J. S., “Consistent Mass Matrix for Distributed Mass Systems,” Journal of the Structural Division, ASCE, Vol. 89, No. ST4, Proc. Paper 3591, Aug., 1963, pp. 161–178.
2.
Eisenberger, M., “Constraints for Axial Strains in Plane Frames,” thesis presented to Stanford University, at Stanford, Calif., in Aug., 1979, in partial fulfillment of the requirements for the degree of Civil Engineer.
3.
Eisenberger, M., “Static and Dynamic Analysis of Plane and Space Frames with Axial Constraints,” Technical Report 48, J. A. Blume Earthquake Engineering Center, Stanford, Calif., Oct., 1980.
4.
Gallagher, R. H., Finite Element Analysis Fundamentals, Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1975.
5.
Gere, J. M., and Weaver, W., Jr., Matrix Algebra for Engineers, Van Nostrand, New York, N.Y., 1967.
6.
Greene, B. E., “Application of Generalized Constraints in the Stiffness Method of Structural Analysis,” AIAA Journal, Vol. 4, No. 9, Sept., 1966, pp. 1531–1537.
7.
Guyan, R. J., “Reduction of Stiffness and Mass Matrices,” AIAA Journal, Vol. 3, No. 2, 1965, p. 380.
8.
Hurty, W. C., “Dynamic Analysis of Structural Systems Using Component Modes,” AIAA Journal, Vol. 3, No. 4, 1965, pp. 678–685.
9.
Timoshenko, S., Young, D. H., and Weaver, W., Jr., Vibration Problems in Engineering, 4th edition, John Wiley and Sons, Inc., New York, N.Y., 1974.
10.
Walton, W. C., Jr., and Steeves, E. C., “A New Matrix Theorem and Its Application for Establishing Independent Coordinates for Complex Dynamic Systems with Constraints,” TR R‐326, National Aeronautics and Space Administration, Oct., 1969.
11.
Weaver, W., Jr., “Constraints for Axial Strains in Frames,” Journal of the Structural Division, ASCE, Vol. 106, No. ST1, Proc. Paper 15121, Jan., 1980, pp. 199–209.
12.
Weaver, W., Jr., and Gere, J. M., Matrix Analysis of Framed Structures, 2nd edition, Van Nostrand, New York, N.Y., 1980.
13.
Weaver, W., Jr., Nelson, M. F., and Manning, T. A., “Dynamics of Tier Buildings,” Journal of the Engineering Mechanics Division, ASCE, Vol. 94, No. EM6, Proc. Paper 6293, Dec., 1968, pp. 1455–1474.
Information & Authors
Information
Published In
Copyright
Copyright © 1983 ASCE.
History
Published online: Mar 1, 1983
Published in print: Mar 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.