Reduced Model Approximation Approach Using Model Updating Methodologies
Publication: Journal of Engineering Mechanics
Volume 144, Issue 3
Abstract
Model reduction has been performed for several decades to allow for correlation of an analytical model to experimental data at a reduced number of points; however, traditional approaches have limitations. Static stiffness matrix reduction methods (e.g., Guyan) may not accurately capture the system dynamics, while techniques based on mode shapes [e.g., the system equivalent reduction expansion process (SEREP)] may experience rank deficiency issues. A new model reduction approach presented herein addresses these limitations by combining the accuracy of SEREP with the full-rank attributes of Guyan reduction. The advantages of the presented methodology over traditional reduction techniques are showcased via analytical studies on a cantilevered beam and general plate-type structure.
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Acknowledgments
Some of the work presented herein was partially funded by Air Force Research Laboratory Award No. FA8651-10-1-0009, “Development of Dynamic Response Modeling Techniques for Linear Modal Components.” Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the particular funding agency. The authors are grateful for the support obtained.
References
ABAQUS [Computer software]. Dassault Systemes, Waltham, MA.
Avitabile, P., Tsuji, H., O’Callahan, J., and DeClerck, J. P. (2004). “Reallocation of system mass and stiffness for achieving target specifications.” Int. J. Veh. Noise Vib., 1(1–2), 97–121.
Bampton, M. C., and Craig, R. R. (1968). “Coupling of substructures for dynamic analyses.” AIAA J., 6(7), 1313–1319.
Baruch, M. (1978). “Optimization procedure to correct stiffness and flexibility matrices using vibration tests.” AIAA J., 16(11), 1208–1210.
Baruch, M., and Bar Itzhack, I. Y. (1978). “Optimal weighted orthogonalization of measured modes.” AIAA J., 16(4), 346–351.
Berman, A. (1979). “Mass matrix correction using an incomplete set of measured modes.” AIAA J., 17(10), 1147–1148.
Berman, A., and Nagy, E. (1983). “Improvement of a large analytical model using test data.” AIAA J., 21(8), 1168–1173.
FEMAP version 9.0 [Computer software]. UGS Corporation, Plano, TX.
FEMtools version 3.0 [Computer software]. Dynamic Design Solutions, Leuven, Belgium.
Guyan, R. J. (1965). “Reduction of stiffness and mass matrices.” AIAA J., 3(2), 380.
Kammer, D. C. (1991a). “A hybrid approach to test-analysis-model development for large space structures.” J. Vib. Acoust., 113(3), 325.
Kammer, D. C. (1991b). “Sensor placement for on-orbit modal identification and correlation of large space structures.” J. Guid. Control Dyn., 14(2), 251–259.
Kidder, R. L. (1973). “Reduction of structural frequency equations.” AIAA J., 11(6), 892.
Leung, A. Y. T. (1978). “An accurate method of dynamic condensation in structural analysis.” Int. J. Numer. Methods Eng., 12(11), 1705–1715.
Marinone, T., Butland, A., and Avitabile, P. (2012). “A reduced model approximation approach using model updating methodologies.” Topics in Modal Analysis II, Volume 6: Proc., 30th IMAC, A Conf. on Structural Dynamics, 2012, R. Allemang, J. De Clerck, C. Niezrecki, and J. R. Blough, eds., Springer, New York, 625–636.
MATLAB [Computer software]. MathWorks, Natick, MA.
Newmark, N. M. (1959). “A method of computation for structural dynamics.” J. Eng. Mech. Div., 85(3), 67–94.
O’Callahan, J. (1986). “MAT_SAP/MATRIX: A general linear algebra operation program for matrix analysis.” Univ. of Massachusetts Lowell, Lowell, MA.
O’Callahan, J. (1989). “A procedure for an improved reduced system (IRS) model.” Proc., 7th Int. Modal Analysis Conf., Society for Experimental Mechanics, Bethel, CT, 17–21.
O’Callahan, J., Avitabile, P., and Riemer, R. (1989). “System equivalent reduction expansion process (SEREP).” Proc., 7th Int. Modal Analysis Conf., Union College, Schenectady, New York, 29–37.
O’Callahan, J., and Leung, R. (1985). “Optimisation of mass and stiffness matrices using a generalised inverse technique on the measured modes.” Proc., 3rd Int. Modal Analysis Conf., Society for Experimental Mechanics, Bethel, CT.
O’Callahan, J., and Li, P. (1995). “The effects of modal vector expansion on finite element model updating.” Proc., 13th Int. Modal Analysis Conf., Society for Experimental Mechanics, Bethel, CT.
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©2018 American Society of Civil Engineers.
History
Received: Jun 1, 2016
Accepted: Sep 15, 2017
Published online: Jan 11, 2018
Published in print: Mar 1, 2018
Discussion open until: Jun 11, 2018
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