Dynamically Modified Linear Structures: Deterministic and Stochastic Response
Publication: Journal of Engineering Mechanics
Volume 122, Issue 11
Abstract
In the dynamical analysis structural modifications often appear for many reasons such as designer structural alterations, and discrepancies between predicted and measured properties of the structures. Furthermore, sometimes evaluating the eigenproperties of several structural systems, as non-classically damped structures or structural systems composed by a primary and a light secondary substructure, requires the adoption of the perturbation approach by considering the real structure as a modification of the original structure. In this paper an unconditionally stable step-by-step procedure able to evaluate both deterministic and stochastic responses of linear structural systems with dynamical modifications is presented. The proposed procedure overcomes the numerical drawbacks connected with the evaluation of the complex eigenproperties of the modified structure. The procedure is based on evaluating in approximate form the fundamental operator of the numerical procedure, either by a closed form expression or by an always convergent Taylor series, as a function of the transition matrix of the unmodified structure.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bathe, K. J., and Wilson, E. L. (1976). Numerical methods in finite element analysis . Prentice-Hall, Inc., Englewood Cliffs, N.J.
2.
Bellman, R. (1974). Introduction to matrix analysis . McGraw-Hill Book Co., New York, N.Y.
3.
Belytschko, T., and Hughes, T. J. R. (1983). Computational methods for transient analysis . North-Holland, Amsterdam, The Netherlands.
4.
Borino, G., and Muscolino, G.(1986). “Mode-superposition methods in dynamic analysis of classically and non-classically damped linear systems.”Earthquake Engrg. Struct. Dyn., 14, 705–717.
5.
Brandon, J. A. (1990). “Strategies for structural dynamic modification.”Res. Studies Press LTD, John Wiley and Sons, Inc., New York, N.Y.
6.
Caughey, T. K., and Ma, F.(1993). “Complex modes and solvability of nonclassical linear systems.”J. Appl. Mech., ASME, 60, 26–28.
7.
Collar, A. R., and Simpson, A. (1987). “Matrices and engineering dynamics.” Ellis Horwood, Ltd., Chichester, England.
8.
Cronin, D. L.(1990). “Eigenvalue and eigenvector determination for nonclassically damped dynamic systems.”Comp. Struct., 36, 133–138.
9.
D'Aveni, A., and Muscolino, G.(1995). “Response of non-classically damped structures in the modal subspace.”Earthquake Engrg. Struct. Dynamics, 24, 1267–1281.
10.
Di Paola, M., and Muscolino, G.(1990). “Differential moment equations of FE modelled structures with geometrical non-linearities.”Int. J. Non-linear Mech., 25, 363–373.
11.
Ewins, D. J. (1991). Modal testing: theory and practice . Research Studies Press LTD, John Wiley and Sons, Inc., New York, N.Y.
12.
Falsone, G., Muscolino, G., and Ricciardi, G.(1992). “Stochastic response of combined primary-secondary structures under seismic input.”Earthquake Engrg. Struct. Dynamics, 21, 927–943.
13.
Harichandran, R. S., and Zhang, Y.(1989). “Eigenproperties of non-classically damped MDOF composite systems.”J. Engrg. Mech., ASCE, 115, 1527–1542.
14.
Kwak, M. K.(1993). “Perturbation method for the eigenvalue problem of lightly damped systems.”J. Sound Vibrations, 160, 351–357.
15.
Meirovitch, L. (1980). “Computational methods in structural dynamics.” Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands.
16.
Muller, P. C., and Schiehlen, W. O. (1985). “Linear vibrations.” Martinus Nijthoff, Dordrecht, The Netherlands.
17.
Smith, M. J., and Hutton, S. C.(1994). “A perturbation method for inverse frequency modification of discrete undamped systems.”J. Appl. Mech., ASME, 61, 887–892.
18.
Suarez, L. E., and Singh, M. P.(1987). “Eigenproperties of non-classically damped primary structure and equipment systems by a perturbation approach.”Earthquake Engrg. Struct. Dyn., 15, 565–583.
19.
Szidarovszky, F., and Bahill, A. T. (1991). Linear systems theory . CRC Press, Boca Raton, Fla.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 122 • Issue 11 • November 1996
Pages: 1044 - 1051
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Nov 1, 1996
Published in print: Nov 1996
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.