SpringerLink
Log in

Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work. With the reservation of the axial nonlinear strain, there are more coupling terms for axial and transverse deformations. The discretized dynamic governing equations are obtained by using the finite element method and Lagrange’s equations of the second kind. Time responses are conducted to compare the proposed model with other previous models. The stretching deformation due to rotating motion is observed and calculated by special formulations under dynamic equilibrium. The stretching deformation and the change of the associated equilibrium position are taken into account to analyze the free vibration and frequency response of the rotating beams. Analytical and numerical comparisons show that the proposed model can provide reliable results, while the previous models may lead to imprecise results, especially in high-speed conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. KANE, T. R., RYAN, R. R., and BANERJEER, A. K. Dynamics of a cantilever beam attached to a moving base. Journal of Guidance, Control, and Dynamics, 10, 139–151 (1987)

    Article  Google Scholar 

  2. YOO, H. H. and SHIN, S. H. Vibration analysis of rotating cantilever beams. Journal of Sound and Vibration, 212, 807–828 (1998)

    Article  Google Scholar 

  3. CHUNG, J. and YOO, H. H. Dynamic analysis of a rotating cantilever beam by using the finite element method. Journal of Sound and Vibration, 249, 147–164 (2002)

    Article  Google Scholar 

  4. KIM, H. and CHUNG, J. Nonlinear modeling for dynamic analysis of a rotating cantilever beam. Nonlinear Dynamics, 86, 1981–2002 (2016)

    Article  Google Scholar 

  5. YANG, J. B., JIANG, J. B., and CHEN, D. C. Dynamic modelling and control of a rotating Euler-Bernoulli beam. Journal of Sound and Vibration, 274, 863–875 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. AL-QAISIA, A. A. and AL-BEDOOR, B. O. Evaluation of different methods for the consideration of the effect of rotation on the stiffening of rotating beams. Journal of Sound and Vibration, 280, 531–553 (2005)

    Article  Google Scholar 

  7. KAYA, M. O. and OZGUMUS, O. O. Energy expressions and free vibration analysis of a rotating uniform Timoshenko beam featuring bending-torsion coupling. Journal of Vibration and Control, 16, 915–934 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. BANERJEE, J. R. Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method. Journal of Sound and Vibration, 233, 857–875 (2000)

    Article  MATH  Google Scholar 

  9. BANERJEE, J. R. Dynamic stiffness formulation and free vibration analysis of centrifugally stiffened Timoshenko beams. Journal of Sound and Vibration, 247, 97–115 (2001)

    Article  Google Scholar 

  10. BANERJEE, J. R. and KENNERDY, D. Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects. Journal of Sound and Vibration, 333, 7299–7312 (2014)

    Article  Google Scholar 

  11. ZENG, J., MA, H., YU, K., XU, Z. T., and WEN, B. C. Coupled flapwise-chordwise-axialtorsional dynamic responses of rotating pre-twisted and inclined cantilever beams subject to the base excitation. Applied Mathematics and Mechanics (English Edition), 40(6), 1053–1082 (2019) https://doi.org/10.1007/s10483-019-2506-6

    Article  MathSciNet  MATH  Google Scholar 

  12. WANG, L. S., SU, Z., and WANG, L. F. Flutter analysis of rotating beams with elastic restraints. Applied Mathematics and Mechanics (English Edition), 43(5), 761–776 (2022) https://doi.org/10.1007/s10483-022-2850-6

    Article  MathSciNet  MATH  Google Scholar 

  13. VIGNERON, F. R. Comment on “Mathematical modeling of spinning elastic bodies for modal analysis”. AIAA Journal, 13, 126–127 (1975)

    Article  Google Scholar 

  14. LIU, J. Y. and HONG, J. Z. Dynamic modeling and modal truncation approach for a high-speed rotating elastic beam. Archive of Applied Mechanics (Ingenieur Archiv), 72, 554–563 (2002)

    Article  MATH  Google Scholar 

  15. YANG, H., HONG, J. Z., and YU, Z. Dynamics modelling of a flexible hub-beam system with a tip mass. Journal of Sound and Vibration, 266, 759–774 (2003)

    Article  Google Scholar 

  16. CAI, G. P., HONG, J. Z., and YANG, S. X. Dynamic analysis of a flexible hub-beam system with tip mass. Mechanics Research Communications, 32, 173–190 (2005)

    Article  MATH  Google Scholar 

  17. LI, L., ZHANG, D. G., and ZHU, W. D. Free vibration analysis of a rotating hub-functionally graded material beam system with the dynamic stiffening effect. Journal of Sound and Vibration, 333, 1526–1541 (2014)

    Article  Google Scholar 

  18. SHARF, I. Geometrically non-linear beam element for dynamics simulation of multibody systems. International Journal for Numerical Methods in Engineering, 39, 763–786 (1996)

    Article  MATH  Google Scholar 

  19. ARVIN, H. and BAKHTIARI-NEJAD, F. Non-linear modal analysis of a rotating beam. International Journal of Non-Linear Mechanics, 46, 877–897 (2011)

    Article  Google Scholar 

  20. HUANG, C. L., LIN, W. Y., and HSIAO, K. M. Free vibration analysis of rotating Euler beams at high angular velocity. Computers and Structures, 88, 991–1001 (2010)

    Article  Google Scholar 

  21. WANG, F. X. Model reduction with geometric stiffening nonlinearities for dynamic simulations of multibody systems. International Journal of Structural Stability and Dynamics, 13, 1350046 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. ZHAO, G. W. and WU, Z. G. Coupling vibration analysis of rotating three-dimensional cantilever beam. Computers and Structures, 179, 64–74 (2017)

    Article  Google Scholar 

  23. BERZERI, M. and SHABANA, A. A. Study of the centrifugal stiffening effect using the finite element absolute nodal coordinate formulation. Multibody System Dynamics, 7, 357–387 (2002)

    Article  MATH  Google Scholar 

  24. ZHANG, X. S., ZHANG, D. G., CHEN, S. J., and HONG, J. Z. Modal characteristics of a rotating flexible beam with a concentrated mass based on the absolute nodal coordinate formulation. Nonlinear Dynamics, 88, 61–77 (2016)

    Article  Google Scholar 

  25. CHEN, Y. Z., ZHANG, D. G., and LI, L. Dynamic analysis of rotating curved beams by using absolute nodal coordinate formulation based on radial point interpolation method. Journal of Sound and Vibration, 441, 63–83 (2019)

    Article  Google Scholar 

  26. THOMAS, O., SENECHAL, A., and DEU, J. F. Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams. Nonlinear Dynamics, 86, 1293–1318 (2016)

    Article  Google Scholar 

  27. PESHECK, E., PIERRE, C., and SHAW, S. W. Modal reduction of a nonlinear rotating beam through nonlinear normal modes. Transactions of ASME Journal of Vibration and Acoustics, 124, 229–236 (2002)

    Article  Google Scholar 

  28. KIM, H., YOO, H. H., and CHUNG, J. Dynamic model for free vibration and response analysis of rotating beams. Journal of Sound and Vibration, 332, 5917–5928 (2013)

    Article  Google Scholar 

  29. SIMO, J. C. and VU-QUOC, L. The role of non-linear theories in transient dynamic analysis of flexible structures. Journal of Sound and Vibration, 119, 487–508 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  30. BEKHOUCHA, F., RECHAK, S., DUIGOU, L., and CADOU, J. M. Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity. Journal of Sound and Vibration, 379, 177–190 (2016)

    Article  Google Scholar 

  31. LEE, S. Y., SHEU, J. J., and LIN, S. M. In-plane vibrational analysis of rotating curved beam with elastically restrained root. Journal of Sound and Vibration, 315, 1086–1102 (2008)

    Article  Google Scholar 

  32. TRINDADE, M. A. and SAMPAIO, R. Dynamics of beams undergoing large rotations accounting for arbitrary axial deformation. Journal of Guidance, Control, and Dynamics, 25, 634–643 (2002)

    Article  Google Scholar 

Download references

Funding

Project supported by the National Natural Science Foundation of China (Nos. 12232012, 12202110, 12102191, and 12072159), the Fundamental Research Funds for the Central Universities of China (No. 30922010314), and the Natural Science Foundation of Guangxi Province of China (No. 2020GXNSFBA297010)

Author information

Authors and Affiliations

  1. School of Science, Nan**g University of Science and Technology, Nan**g, 210094, China

    **aokang Du, **g Zhang, **an Guo, Liang Li & Dingguo Zhang

  2. School of Mechanical and Automotive Engineering, Guangxi University of Science and Technology, Liuzhou, Guangxi Province, 545006, China

    Yuanzhao Chen

Authors
  1. **aokang Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanzhao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. **g Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. **an Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Liang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Dingguo Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dingguo Zhang.

Additional information

Citation: DU, X. K., CHEN, Y. Z., ZHANG, J., GUO, X., LI, L., and ZHANG, D. G. Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect. Applied Mathematics and Mechanics (English Edition), 44(1), 125–140 (2023) https://doi.org/10.1007/s10483-023-2951-9

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, X., Chen, Y., Zhang, J. et al. Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect. Appl. Math. Mech.-Engl. Ed. 44, 125–140 (2023). https://doi.org/10.1007/s10483-023-2951-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-023-2951-9

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation