Random Uncertainties Model in Dynamic Substructuring Using a Nonparametric Probabilistic Model
Publication: Journal of Engineering Mechanics
Volume 129, Issue 4
Abstract
This paper presents a new approach, called a nonparametric approach, for constructing a model of random uncertainties in dynamic substructuring in order to predict the matrix-valued frequency response functions of complex structures. Such an approach allows nonhomogeneous uncertainties to be modeled with the nonparametric approach. The Craig–Bampton dynamic substructuring method is used. For each substructure, a nonparametric model of random uncertainties is introduced. This nonparametric model does not require identifying uncertain parameters in the reduced matrix model of each substructure as is usually done for the parametric approach. This nonparametric model of random uncertainties is based on the use of a probability model for symmetric positive-definite real random matrices using the entropy optimization principle. The theory and a numerical example are presented in the context of the finite-element method. The numerical results obtained show the efficiency of the model proposed.
Get full access to this article
View all available purchase options and get full access to this article.
References
Anderson, T. W. (1958). Introduction to multivariate statistical analysis, Wiley, New York.
Argyris, J., and Mlejnek, H. P. (1991). Dynamics of structures, North-Holland, Amsterdam.
Bathe, K. J., and Wilson, E. L. (1976). Numerical methods in finite element analysis, Prentice-Hall, New York.
Benfield, W. A., and Hruda, R. F.(1971). “Vibration analysis of structures by component mode substitution.” AIAA J., 9, 1255–1261.
Cheung, Y. K., and Leung, A. Y. T. (1992). Finite element methods in dynamics, Kluwer Academic, Dordrecht, The Netherlands.
Clough, R. W., and Penzien, J. (1975). Dynamics of structures, McGraw-Hill, New York.
Cochran, W. G. (1977). Sampling techniques, Wiley, New York.
Craig, R. R., and Bampton, M. M. C.(1968). “Coupling of substructures for dynamic analysis.” AIAA J., 6, 1313–1319.
Géradin, M., and Rixen, D. (1994). Mechanical vibrations, Wiley, Chichester, U.K.
Ghanem, R. G., and Spanos, P. D. (1991). Stochastic finite elements: A spectral approach, Springer, New York.
Haug, E. J., Choi, K. K., and Komkov, V. (1986). Design sensitivity analysis of structural systems, Academic, New York.
Hintz, R. M.(1975). “Analytical methods in component modal synthesis.” AIAA J., 13, 1007–1016.
Hurty, W. C.(1965). “Dynamic analysis of structural systems using component modes.” AIAA J., 3(4), 678–685.
Ibrahim, R. A. (1985). Parametric random vibration, Wiley, New York.
Ibrahim, R. A.(1987). “Structural dynamics with parameter uncertainties.” Appl. Mech. Rev., 40(3), 309–328.
Iwan, W. D., and Jensen, H. (1993). “On the dynamic response of continuous systems including model uncertainty.” Trans. ASME, 60, 484–490.
Jaynes, E. T.(1957). “Information theory and statistical mechanics.” Phys. Rev., 106(4), 620–630;
IBID1957108(2), 171–190.
Kalos, M. H., and Whitlock, P. A. (1986). Monte Carlo methods, Vol. 1: Basics, Wiley, New York.
Kapur, J. N., and Kesavan, H. K. (1992). Entropy optimization principles with applications, Academic, San Diego.
Kleiber, M., Tran, D. H., and Hien, T. D. (1992). The stochastic finite element method, Wiley, New York.
Kree, P., and Soize, C. (1986). Mathematics of random phenomena, Reidel, Dordrecht, The Netherlands.
Lee, C., and Singh, R.(1994). “Analysis of discrete vibratory systems with parameter uncertainties. Part II. Impulse response.” J. Sound Vib., 174(3), 395–412.
Lin, Y. K., and Cai, G. Q. (1995). Probabilistic structural dynamics, McGraw-Hill, New York.
Liu, W. K., Belytschko, T., and Mani, A.(1986). “Random field finite elements.” Int. J. Numer. Methods Eng., 23, 1832–1845.
MacNeal, R.H.(1971). “A hybrid method of component mode synthesis.” AIAA J., 1, 581–601.
Mehta, M. L. (1991). Random matrices, revised and enlarged 2nd Ed., Academic, New York.
Meirovitch, L. (1980). Computational methods in structural dynamics, Sijthoff and Noordhoff, The Netherlands.
Meirovitch, L., and Hale, L.(1981). “On the substructure synthesis method.” AIAA J., 19, 940–947.
Morand, H. P. J., and Ohayon, R.(1979). “Substructure variational analysis for the vibrations of coupled fluid-structure systems.” Int. J. Numer. Methods Eng., 14(5), 741–755.
Ohayon, R., and Soize, C. (1998). Structural acoustics and vibration, Academic, San Diego.
Roberts, J. B., and Spanos, P. D. (1990). Random vibration and statistical linearization, Wiley, New York.
Rubin, S.(1975). “Improved component-mode representation for structural dynamic analysis.” AIAA J., 13, 995–1006.
Rubinstein, R. Y. (1981). Simulation and the Monte Carlo method, Wiley, New York.
Shannon, C. E.(1948). “A mathematical theory of communication.” Bell Syst. Tech. J., 27, 379–423;
IBID194827, 623–659.
Shinozuka, M., and Deodatis, G.(1988). “Response variability of stochastic finite element systems.” J. Eng. Mech., 114(3), 499–519.
Soize, C. (1994). The Fokker–Planck equation for stochastic dynamical systems and its explicit steady state solutions, World Scientific, Singapore.
Soize, C. (1999). “A nonparametric model of random uncertainties in linear structural dynamics.” Publication du LMA-CNRS, 152, 109–138.
Soize, C.(2000). “A nonparametric model of random uncertainties for reduced matrix models in structural dynamics.” Probab. Eng. Mech., 15(3), 277–294.
Soize, C.(2001). “Maximum entropy approach for modeling random uncertainties in transient elastodynamics. ” J. Acoust. Soc. Am., 109(5), 1979–1996.
Soize, C., and Bjaoui, K.(2000). “Estimation of fuzzy structure parameters for continuous junctions.” J. Acoust. Soc. Am., 107(4), 2011–2020.
Soong, T. T. (1973). Random differential equations in science and engineering, Academic, New York.
Spanos, P. D., and Ghanem, R. G.(1989). “Stochastic finite element expansion for random media.” ASCE J. Eng. Mech.,115(5), 1035–1053.
Spanos, P. D., and Zeldin, B. A.(1994). “Galerkin sampling method for stochastic mechanics problems.” J. Eng. Mech., 120(5), 1091–1106.
Vanmarcke, E., and Grigoriu, M.(1983). “Stochastic finite element analysis of simple beams.” J. Eng. Mech., 109(5), 1203–1214.
Zienkiewicz, O. C., and Taylor, R. L. (1989). The finite element method, 4th Ed., McGraw-Hill, New York.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 129 • Issue 4 • April 2003
Pages: 449 - 457
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: May 11, 2001
Accepted: Sep 20, 2002
Published online: Mar 14, 2003
Published in print: Apr 2003
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.