APPLICATION OF THE CRAIG-BAMPTON MODEL ORDER REDUCTION METHOD TO A COMPOSITE STRUCTURE: MAC AND XOR

Abstract The Craig-Bampton model order reduction (CBMOR) method based on the Rayleigh-Ritz approach is applied to dynamic behavior simulation of a composite structure in order to verify the method’s feasibility and accuracy. The principle of this method is to represent a coupled component model based on the mass, damping and stiffness matrices. The methodology consists of a finite element model based on the classical laminate theory (CLT), a design of experiment to improve the modal assurance criteria (MAC) and experimental results in order to validate the reduced model based on CBMOR method and substructures (super-elements). Experimental modal analysis has been performed using a scanner laser Doppler vibrometer (SLDV) in order to assess the quality of the finite element models. The MAC and cross orthogonality MAC (XOR) values are computed to verify the eigenfrequencies and eigenvectors. This approach demonstrates the feasibility of using CBMOR for composite structures. The example is prepared and solved with MSC/NASTRAN SOL103. The design of experiments (DOE) method has been applied in order to identify the critical parameters and thus obtain high MAC values. References Hurty, W. C., 1965, Dynamic analysis of structural systems using component modes, AIAA Journal, 3(4), pp. 678-685. Craig R. J. and Bampton M., 1968, Coupling of substructures for dynamic analyses, AIAA Journal 6(7), pp.1313-1319. SDTools Inc. 2011, Structural dynamics toolbox and FEMLink, User's Guide, SDTools, Ver. 6.4, Paris, France. Guyan, J. 1965, Reduction of stiffness and mass matrices, AIAA Journal, 3(380). pp. Irons, B. M.., 1965, Structural eigenvalue problems - elimination of unwanted variables, AIAA Journal, 3(5): pp. 961-962. Balmès E., 1996, Use of generalized interface degrees of freedom in component mode synthesis, International Modal Analysis Conference, pp. 204-210. Montgomery, D. C., 2000, Design and analysis of experiments, John Wiley & Sons. Fan J., Zeng, W., Wang R., Sherr X., Chen Z., 2010, Research on design and optimization of the turbine blade shroud, 2nd International Conference on Engineering Optimization, Lisbon, Portugal. Barner, N., 2010, Isight-Abaqus optimization of a ring-stiffened Cylinder, SIMULIA Customer Conference. Chen, X., Yu, X., and Ji B., 2010, Study of crankshaft strength based on iSIGHT platform and DOE methods, International Conference on Measuring Technology and Mechatronics Automation, pp. 548-551. Lauwagie, T., 2005, Vibration-Based Methods for the Identification of the Elastic Properties of Layered Materials, PhD thesis, Catholic University of Leuven, Belgium. Reddy, J. N., 2005, Mechanics of Laminated Composite Plates and Shells Theory and Analysis, CRC, Press Second edition. Berthelot, J. M., 1992, Materiaux composites: Comportement mecanique et analyse des structures, Lavoisier, Paris, France Balmès E., 1997, Efficient Sensitivity Analysis Based on Finite Element Model Reduction, International Modal Analysis Conference, IMAC, pp.1-7. Balmès E., 1996, Frequency domain identification of structural dynamics using the pole/residue parametrization, International Modal Analysis Conference, pp. 540-546. Gade, S., Møller, N.B., Jacobsen, N.J., and Hardonk. B., 2000, Modal analysis using a scanning laser Doppler vibrometer, Sound and Vibration Measurements, pp. 1015-1019. Newland, D.E., 1993, An Introduction to random vibration, spectral and wavelet Analysis, New York, Longman, Harlow and John Wiley. Ewings, D. J., 1995, Modal testing: Theory and practice, Research Studies Press, Letchworth, United Kingdom. Cunedioğlu, Y., Muğan, A., Akçay, H., 2006, Frequency domain analysis of model order reduction techniques, Finite Elements in Analzsis and Design, 42, pp. 367-403. Batoz, J.L., Bathe, K.J., Ho, L.W., 1980, A Study of three node triangular plate bending elements, International Journal for Numerical Methods in Engineering, 15, pp. 1771-1812. Batoz, J.L., Lardeur, P., 1989, Composite plate analysis using a new discrete shear triangular finite element, International Journal for Numerical Methods in Engineering, 27, pp. 343-359. Craig, R.J., 1987, A review of time-domain and frequency domain component mode synthesis methods. Int. J. Anal. and Exp. Modal Analysis, 2(2), pp. 59-72. Balmès, E., 2000, Review and Evaluation of shape expansion methods, International Modal Analysis Conference, pp. 555-561. Bonisoli E, Delprete C., Espoito M., Mottershead J. E., 2011, Structural Dynamics with conicident Eigenvalues: Modeling and Testing, Modal Analysis Topics 3, pp 325-337. Pierre C., 1988, Mode Localization and eigenvalue loci of Bridges with Aeroeslastic effects, Journal of Engineering Mechanics 126(3), pp. 485-502.