An extended Craig-Bampton method for the modal analysis of mechanisms

  • Alessandro CammarataEmail author
  • Rosario Sinatra
  • Pietro Davide Maddio
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


In this paper, an extended Craig-Bampton method is proposed. Despite the common procedure widely used in structural dynamics to create superelements to be combined by means of joints; here, the joints are included in the reduction procedure. This novelty makes it possible to obtain larger superelements that might be subparts of a mechanism or even the whole mechanism. Starting from the classic Craig-Bampton method, the fixed-interface normal modes and interface constraint modes are redefined including the joints contribution. A new transformation matrix necessary to obtain the reduced stiffness and inertia matrices is presented. Finally, the case study of a deployable mechanism is studied. The results of numerical calculations are compared for validation with ANSYS® results.


Component mode synthesis dynamic substructuring modal analysis flexible mechanical systems fixed interface 


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  1. 1.
    Hurty, W.C.: Dynamic analysis of structural systems using component modes. AIAA journal 3(4), 678–685 (1965)CrossRefGoogle Scholar
  2. 2.
    Craig, R.R., Bampton, M.C.: Coupling of substructures for dynamic analysis. AIAA journal 6(7), 1313–1319 (1968)Google Scholar
  3. 3.
    Kubomura, K.: A theory of substructure modal synthesis. ASME, Transactions, Journal of Applied Mechanics 49, 903–909 (1982)CrossRefGoogle Scholar
  4. 4.
    Suarez, L., Singh, M.: Improved fixed interface method for modal synthesis. AIAA journal 30(12), 2952–2958 (1992)CrossRefGoogle Scholar
  5. 5.
    Kim, J.G., Lee, P.S.: An enhanced craig–bampton method. International Journal for Numerical Methods in Engineering 103(2), 79–93 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Boo, S.H., Kim, J.H., Lee, P.S.: Towards improving the enhanced craig-bampton method. Computers & Structures 196, 63–75 (2018)Google Scholar
  7. 7.
    Carassale, L., Maurici, M.: Interface reduction in craig–bampton component mode synthesis by orthogonal polynomial series. Journal of Engineering for Gas Turbines and Power 140(5), 052,504 (2018)CrossRefGoogle Scholar
  8. 8.
    Krattiger, D., Wu, L., Zacharczuk, M., Buck, M., Kuether, R.J., Allen, M.S., Tiso, P., Brake, M.R.: Interface reduction for hurty/craig-bampton substructured models: Review and improvements. Mechanical Systems and Signal Processing 114, 579–603 (2019)CrossRefGoogle Scholar
  9. 9.
    Park, K., Park, Y.H.: Partitioned component mode synthesis via a flexibility approach. AIAA journal 42(6), 1236–1245 (2004)CrossRefGoogle Scholar
  10. 10.
    Markovic, D., Park, K., Ibrahimbegovic, A.: Reduction of substructural interface degrees of freedom in flexibility-based component mode synthesis. International journal for numerical methods in engineering 70(2), 163–180 (2007)CrossRefGoogle Scholar
  11. 11.
    Cammarata, A., Condorelli, D., Sinatra, R.: An algorithm to study the elasto-dynamics of parallel kinematic machines with lower kinematic pairs. Journal of Mechanisms and Robotics 5(1), 011,004 (2013)CrossRefGoogle Scholar
  12. 12.
    Cammarata, A.: Unified formulation for the stiffness analysis of spatial mechanisms. Mechanism and Machine Theory 105, 272–284 (2016)CrossRefGoogle Scholar
  13. 13.
    Alessandro, C., Rosario, S.: Elastodynamic optimization of a 3t1r parallel manipulator. Mechanism and Machine Theory 73, 184–196 (2014)CrossRefGoogle Scholar
  14. 14.
    Cammarata, A., Sinatra, R.: On the elastostatics of spherical parallel machines with curved links. In: Recent Advances in Mechanism Design for Robotics, pp. 347–356. Springer (2015)Google Scholar
  15. 15.
    Cammarata, A., Cali`o, I., Greco, A., Lacagnina, M., Fichera, G., et al.: Dynamic stiffness model of spherical parallel robots. Journal of Sound and Vibration 384, 312–324 (2016)CrossRefGoogle Scholar
  16. 16.
    Cammarata, A.: A novel method to determine position and orientation errors in clearance-affected overconstrained mechanisms. Mechanism and Machine Theory 118, 247–264 (2017)CrossRefGoogle Scholar
  17. 17.
    Maddio, P., Meschini, A., Sinatra, R., Cammarata, A.: An optimized form-finding method of an asymmetric large deployable reflector. Engineering Structures 181, 27–34 (2019)CrossRefGoogle Scholar
  18. 18.
    Qu, Z.Q.: Model order reduction techniques with applications in finite element analysis. Springer Science & Business Media (2013)Google Scholar
  19. 19.
    Bouhaddi, N., Fillod, R.: Model reduction by a simplified variant of dynamic condensation. Journal of Sound and Vibration 191(2), 233–250 (1996)CrossRefGoogle Scholar
  20. 20.
    Yee, V.: Reduction of component mode synthesis formulated matrices for correlation studies. AIAA journal 28, 1142–1143 (1990)CrossRefGoogle Scholar
  21. 21.
    Kammer, D.C., Flanigan, C.: Development of test-analysis models for large space structures using substructure representations. Journal of Spacecraft and Rockets (1990)Google Scholar
  22. 22.
    Blades, E.L.: A craig-bampton test-analysis model. In: Proceedings-SPIE the International Society for Optical Engineering, pp. 1386–1391. SPIE International Society for Optical (1997)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alessandro Cammarata
    • 1
    Email author
  • Rosario Sinatra
    • 1
  • Pietro Davide Maddio
    • 1
  1. 1.University of Catania, Dipartimento Ingegneria Civile e ArchitetturaCataniaItaly

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