Advertisement

A Truly Hybrid Approach to Substructuring Problems Using Mixed Assembly and Implicit Solving Strategies

  • S. N. Voormeeren
  • P. L. C. van der Valk
  • D. J. Rixen
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

In recent years, the structural dynamic community showed a renewed interest in component coupling (i.e. dynamic substructuring) and decoupling techniques for structural dynamic analysis of assembled systems. Especially for hybrid problems, where some component models are obtained from experimental data and others from numerical modeling, these techniques offer interesting possibilities. However, since measured models are generally expressed in terms of flexibility and numerical models in terms of stiffness, model inversions are needed at least at the component interfaces. This leads to increased computational effort and/or amplification of measurement errors. To avoid the inversions of the component models, a truly hybrid approach to coupling and decoupling problems is proposed in this paper. Using a mixed assembly methodology derived from a so-called “three field formulation”, stiffness type components can be directly assembled to flexibility based subsystems. Then only the interface problem remains to be solved. In part one of this paper the theoretical derivation of the proposed methodology is addressed. Furthermore, we outline the differences with respect to the existing methods.

Keywords

Mode Shape Frequency Response Function Experimental Mechanics Dynamic Stiffness Interface Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allemang, R., Brown, D.: A Correlation Coefficient for Modal Vector Analysis. In: Proceedings of the International Modal Analysis Conference, pp. 110–116. Society for Experimental Mechanics (1982)Google Scholar
  2. 2.
    Allen, M., Mayes, R.: Comparison of FRF and Modal Methods for Combining Experimental and Analytical Substructures. In: Proceedings of the Twentyfifth International Modal Analysis Conference, Orlando, FL. Society for Experimental Mechanics, Bethel, CT (2007)Google Scholar
  3. 3.
    Bregnant, L., Otte, D., Sas, P.: FRF Substructure Synthesis. Evaluation and Validation of Data Reduction Techniques. In: Proceedings of the Twentieth International Conference on Noise & Vibration Engineering (ISMA). Katholieke Universiteit Leuven, Leuven, BE (1995)Google Scholar
  4. 4.
    Campbell, R., Hambric, S.: Application of Frequency Domain Substructure Synthesis Technique for Plates loaded with Complex Attachments. Tech. rep., Pennsylvania State University Park Applied Research Lab (2004)CrossRefGoogle Scholar
  5. 5.
    Carne, T.G., Dohrmann, C.R.: Improving Experimental Frequency Response Function Matrices for Admittance Modeling. In: Proceedings of the Twenty Fourth International Modal Analysis Conference, St. Louis, MO. Society for Experimental Mechanics, Bethel, CT (2006)Google Scholar
  6. 6.
    Corus, M., Balmes, E., Nicolas, O.: Using Model Reduction and Data Expansion Techniques to Improve SDM. Mechanical Systems and Signal Processing 20, 1067–1089 (2006)CrossRefGoogle Scholar
  7. 7.
    Duarte, M., Ewins, D.: Some Insights into the Importance of Rotational Degrees of Freedom and Residual Terms in Coupled Structure Analysis. In: Proceedings of the Thirteenth International Modal Analysis Conference, Nashvill, TN, pp. 164–170. Society for Experimental Mechanics, Bethel, CT (1995)Google Scholar
  8. 8.
    Ferreira, J., Ewins, D.: Multi-Harmonic Nonlinear Receptance Coupling Approach. In: Proceedings of the Fifteenth International Modal Analysis Conference, Orlando, FL, pp. 27–33. Society for Experimental Mechanics, Bethel, CT (1997)Google Scholar
  9. 9.
    Gialamas, T., Tsahalis, D., Bregant, L., Otte, D., van der Auweraer, H.: Substruturing by means of FRFs. Some Investigations on the Significance of Rotational DOFs. In: Proceedings of the Fourteenth International Modal Analysis Conference, Dearborn, MI, pp. 619–625. Society for Experimental Mechanics, Bethel, CT (1996)Google Scholar
  10. 10.
    Hunter, N., Paez, T.: Nonlinear Behavior of a 45 Degree Bolted Lap Joint. In: Proceedings of the Twentyfourth International Modal Analysis Conference, St. Louis, MO. Society for Experimental Mechanics, Bethel, CT (2006)Google Scholar
  11. 11.
    Imregun, M., Robb, D.: Structural Modification via FRF Coupling using Measured Data. In: Proceedings of the Tenth International Modal Analysis Conference, San Diego, CA, pp. 1095–1099. Society for Experimental Mechanics, Bethel, CT (1992)Google Scholar
  12. 12.
    Imregun, M., Robb, D., Ewins, D.: Structural modification and coupling dynamic analysis using measured frf data. In: Proceedings of the Fifth International Modal Analysis Conference, London, UK, pp. 1136–1141. Society for Experimental Mechanics, Bethel, CT (1987)Google Scholar
  13. 13.
    de Klerk, D., Rixen, D., de Jong, J.: The Frequency Based Substructuring (FBS) Method Reformulated According to the Dual Domain Decomposition Method. In: Proceedings of the Twenty Fourth International Modal Analysis Conference, St. Louis, MO. Society for Experimental Mechanics, Bethel, CT (2006)Google Scholar
  14. 14.
    de Klerk, D., Rixen, D., Voormeeren, S.: General Framework for Dynamic Substructuring: History, Review and Classification of Techniques. AIAA Journal 46(5), 1169–1181 (2008)Google Scholar
  15. 15.
    de Klerk, D., Rixen, D., Voormeeren, S., Pasteuning, F.: Solving the RDoF Problem in Experimental Dynamic Substructuring. In: Proceedings of the Twenty Sixth International Modal Analysis Conference, Orlando, FL. Society for Experimental Mechanics, Bethel, CT (2008). Paper no. 129Google Scholar
  16. 16.
    de Klerk, D., Voormeeren, S.: Uncertainty Propagation in Experimental Dynamic Substructuring. In: Proceedings of the Twenty Sixth International Modal Analysis Conference, Orlando, FL. Society for Experimental Mechanics, Bethel, CT (2008). Paper no. 133Google Scholar
  17. 17.
    Lim, T., Li, J.: A Theoretical and Computational Study of the FRF-Based Substructuring Technique applying enhanced Least Square and TSVD Approaches. Journal of Sound and Vibration 231, 1135–1157 (2000)CrossRefGoogle Scholar
  18. 18.
    Liu, W., Ewins, D.: The Importance Assessment of RDOF in FRF Coupling Analysis. In: Proceedings of the Seventeenth International Modal Analysis Conference, Orlando, FL, pp. 1481–1487. Society for Experimental Mechanics, Bethel, CT (1999)Google Scholar
  19. 19.
    Mayes, R., Stasiunas, E.: Combining Lightly Damped Experimental Substructures with Analytical Substructures. In: Proceedings of the Twentyfifth International Modal Analysis Conference, Orlando, FL. Society for Experimental Mechanics, Bethel, CT (2007)Google Scholar
  20. 20.
    Montalvao, D., Ribeiro, A., Maia, N., Silva, J.: Estimation of the Rotational Terms of the Dynamic Response Matrix. Shock and Vibration 11, 333–350 (2004)Google Scholar
  21. 21.
    O’Callahan, J., Avitabile, P., Riemer, R.: System Equivelant Reduction Expansion Process (SEREP). In: Proceedings of the Seven International Modal Analysis Conference, Las Vegas, NV, pp. 29–37. Society for Experimental Mechanics, Bethel, CT (1989)Google Scholar
  22. 22.
    O’Callahan, J., Lieu, I., Chou, C.: Determination of Rotational Degrees of Freedom for Moment Transfers in Structural Modifications. In: Proceedings of the Third International Modal Analysis Conference, Orlando, FL, pp. 465–470. Society for Experimental Mechanics, Bethel, CT (1985)Google Scholar
  23. 23.
    Pasteuning, F.: Experimental Dynamic Substructuring and its Application in Automotive Research – Substructure modelling, measurement and connectivity. Master’s thesis, Delft University of Technology, Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering (2007)Google Scholar
  24. 24.
    Petersen, K.B., Pedersen, M.S.: The matrix cookbook (2008). URL http://matrixcookbook.com
  25. 25.
    Rayleigh, J.: The Theory of Sound. Dover Publications (1896)Google Scholar
  26. 26.
    Rixen, D.: How measurement inaccuracies induce spurious peaks in Frequency Based Substructuring. In: Proceedings of the Twenty Sixth International Modal Analysis Conference, Orlando, FL. Society for Experimental Mechanics, Bethel, CT (2008). Paper no. 87Google Scholar
  27. 27.
    Tosseli, A., Widlund, O.: Domain Decomposition Methods – Algorithms and Theory, vol. 34. Springer (2004)Google Scholar
  28. 28.
    Voormeeren, S., de Klerk, D., Rixen, D.: Uncertainty Quantification in Experimental Frequency Based Substructuring. Mechanical Systems and Signal Processing 24(1), 106–118 (2010). Doi:10.1016/j.ymssp.2009.01.016CrossRefGoogle Scholar
  29. 29.
    Wittrick, W., Williams, F.: A General Algorithm for Computing Natural Frequencies of Elastic Structures. Quart. Journ. Mech. and Applied Math. XXIV, 263–284 (1971)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • S. N. Voormeeren
    • 1
  • P. L. C. van der Valk
  • D. J. Rixen
  1. 1.Delft University of TechnologyDelftthe Netherlands

Personalised recommendations