Abstract
The Craig-Bampton model order reduction (CBMOR) method based on the Rayleigh-Ritz approach was applied in a previous work to simulate dynamic behavior of a composite structure (CFRP) using the modal assurance criteria (MAC) and cross orthogonality (XOR) to validate the correlation. Different coordinate modal assurance criteria are applied to complement and verify the eigenfrequencies and eigenvectors obtained of the full and reduced models using substructures (super-elements). An improvement is observed per paired mode-sensor with the MAC per coordinates criterion (MACco) in a CFRP once the stiffness parameters are updated in the full model applying a mix-numerical experimental technique (MNET) using a design of experiments (DOE). The coordinate modal assurance criteria (COMAC) and the scaleCOMAC (COMACS) results of the full models display the best results respect to the reduced model. Furthermore, slight improvement of the enhanced COMAC (eCOMAC) results are observed in the reduced model despite having lower MAC performance. This approach complements the results of the previous work using several COMAC techniques, and demostrates the feasibility to achieve low COMACs results in the reduced finite element model once the stiffness parameters of the full element model are updated. The example was prepared and solved with MSC/NASTRAN SOL103 and SDTools-MATLAB for comparative purposes.
References
[1] Hurty W.C., Dynamic analysis of structural systems using component modes, AIAA J., 3(4), 1965, 678–685 10.2514/3.2947Search in Google Scholar
[2] Craig R.J., Bampton M., Coupling of substructures for dynamic analyses, AIAA J., 6(7), 1968, 1313–1319 10.2514/3.4741Search in Google Scholar
[3] Balmès E., Structural dynamics toolbox and FEMLink, User’s Guide, SDTools, Paris, France, 2016, http://www.sdtools.com/ help/sdt.pdf Search in Google Scholar
[4] Van der Valk P.L.C., Model Reduction&interface modeling in dynamic substructuring, MSc. thesis, TU Delf, Netherlands, 2010. Search in Google Scholar
[5] Reddy J. N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC, Press Second edition, 2004 10.1201/b12409Search in Google Scholar
[6] Cunedioğlu Y., Muğan A., Akçay H., Frequency domain analysis of model order reduction techniques, Finite Elements in Analysis and Design, 42, 2006, 367–403 10.1016/j.finel.2005.08.005Search in Google Scholar
[7] Balmès E., Optimal Ritz vectors for component mode synthesis using singular value decomposition, AIAA J., 34(5), 1996, 1256– 1260 10.2514/3.13221Search in Google Scholar
[8] Balmès E., Use of generalized interface degrees of freedom in component mode synthesis, IMAC 1996, 204–210 Search in Google Scholar
[9] Balmès E., Eflcient Sensitivity Analysis Based on Finite Element Model Reduction, IMAC 1997, 1–7 Search in Google Scholar
[10] Balmès E., Frequency domain identification of structural dynamics using the pole/residue parametrization, IMAC 1996, 540– 546 Search in Google Scholar
[11] Balmès E., Review and Evaluation of shape expansion methods, IMAC 2000, 555–561 Search in Google Scholar
[12] Balmès E., Modes and regular shapes. How to extend component mode synthesis theory, XI DINAME, 28th February-4th March 2005, 1–14 Search in Google Scholar
[13] Bobillot A., Balmès E., Iterative computation of modal sensitivities. AIAA J., 44(6), 2006, 1332–1338 10.2514/1.11525Search in Google Scholar
[14] Kaplan M., Implementation of Automated Multilevel Substructuring for frequency response Analysis of structures, PhD thesis, The University of Texas at Austin, U.S.A. Search in Google Scholar
[15] Jin-Gyun K., Seung-Hwan B., Phill-Seung L., An enhanced AMLS method and its performance. Computed methods in applied mechanics and engineering, 287, 2015, 90–111 10.1016/j.cma.2015.01.004Search in Google Scholar
[16] Bonisoli E., Delprete C., Espoito M., Mottershead J. E., Structural Dynamics with conicident Eigenvalues: Modeling and Testing, Modal Analysis Topics, 3, Conferencing Proceedings of the Society for Experimental Mechanics Series 6, 2011, 325–337 10.1007/978-1-4419-9299-4_29Search in Google Scholar
[17] Peredo Fuentes H., Zehn M., Application of the Craig-Bampton model order reduction method to a composite component assembly, Facta Universitatis, series: Mechanical Engineering, 12(1), 2014, 37–50 Search in Google Scholar
[18] Meuwissen M.H.H., An inverse method for the mechanical characterization of metals, PhD thesis, Technische University Eindhoven, Netherlands, 1998 Search in Google Scholar
[19] Van Ratingen M.R., Mechanical identification of inhomogeneous solids, PhD thesis, Technische University Eindhoven. Netherlands, 1994 Search in Google Scholar
[20] Gade S., Møller N.B., Jacobsen N.J., and Hardonk B., Modal analysis using a scanning laser Doppler vibrometer, Sound and Vibration Measurements A/S, 2000, 1015–1019 Search in Google Scholar
[21] Ewins D. J., Modal testing: Theory and practice, Research Studies Press, Letchworth, U. K., 1995 Search in Google Scholar
[22] Montgomery D. C., Design and analysis of experiments, 5th ed., John Wiley & Sons Inc., USA, 2000 Search in Google Scholar
[23] Allemang R.J., Brown D.L., A correlation coeflcient for modal vector analysis, IMAC 1982, 110–116 Search in Google Scholar
[24] Lieven N. A.J., Ewins D.J., Spatial correlation of mode shapes, The coordinate modal assurance criterion (COMAC), IMAC 1988, 690–695 Search in Google Scholar
[25] Catbas F.N., Aktan A.E., Allemang R.J., Brown D.L., Correlation function for spatial locations of scaled mode shapes (COMEF), IMAC 1998, 1550–1555 Search in Google Scholar
[26] Hunt D.L., Application of an enhanced coordinate modal assurance criteria (ECOMAC), IMAC 1992, 66–71 Search in Google Scholar
[27] Allemang R.J, The modal assurance criterion – twenty years of use and abuse, Sound and vibration, 2003, 14–21 Search in Google Scholar
[28] Brughmans M., Leuridan J., Blauwkamp K., The application of FEM-EMA correlation and validation techniques on a body-inwhite. IMAC 1993, 646–654 Search in Google Scholar
[29] Batoz J.L., Bathe K.J., Ho L.W., A Study of three node triangular plate bending elements, International Journal for Numerical Methods in Engineering, 15, 1980, 1771–1812 10.1002/nme.1620151205Search in Google Scholar
[30] Batoz J.L., Lardeur P., Composite plate analysis using a new discrete shear triangular finite element, International Journal for Numerical Methods in Engineering, 27, 1989, 343–359 10.1002/nme.1620270209Search in Google Scholar
[31] Pierre C., Mode Localization and eigenvalue loci of Bridges with Aeroeslastic effects, Journal of Engineering Mechanics 126(3), 1988, 485–502 10.1016/0022-460X(88)90226-XSearch in Google Scholar
[32] Schwarz B., Richardson M., Scaling mode shapes obtained from operating data, IMAC 2003, 1–8 Search in Google Scholar
[33] Minitab 17 Statistical Software, Computer software, State College, PA:Minitab, Inc., 2010, (www.minitab.com) Search in Google Scholar
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