Skip to main content
Log in

Vibrational characteristics of rotating soft cylinders

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

Rotating structural components are omnipresent in engineering structures and natural world. This work investigates the effects of the centrifugal and Coriolis forces on the free vibrational characteristics of soft cylinders rotating with respect to the axis of symmetry based on the nonlinear elasticity and linear incremental theories. The formulations indicate that the biasing deformation, instantaneous elastic moduli, and incremental equations of motion strongly depend on the rotating speed. The characteristic equation for the natural frequency is derived using the state-space method and approximate laminate technique. The numerical examples included in this work demonstrate that the centrifugal and Coriolis forces might have significant effects on the vibrational characteristics of the cylinder. Results of this work will benefit the design and control of novel engineering systems with rotating soft cylinders or shafts.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Zhang, and Z. Wu, Asian J. Water Environ. Pollut. 2, 27 (2005).

    Google Scholar 

  2. R. J. Mair, Géotechnique 58, 695 (2008).

    Article  Google Scholar 

  3. H. Zhao, L. Shao, and J. F. Chen, Chem. Eng. J. 156, 588 (2010).

    Article  Google Scholar 

  4. G. Clément, npj Microgr. 3, 29 (2017).

    Article  Google Scholar 

  5. W. Yang, H. T. Wang, T. F. Li, and S. X. Qu, Sci. China-Phys. Mech. Astron. 62, 14601 (2019).

    Article  ADS  Google Scholar 

  6. D. Wu, Y. J. Yin, H. M. Xie, Y. F. Shang, C. W. Li, L. F. Wu, and X. L. Dai, Sci. China-Phys. Mech. Astron. 57, 637 (2014).

    Article  ADS  Google Scholar 

  7. S. Mora, and F. Richard, Int. J. Solids Struct. 167, 142 (2019).

    Article  Google Scholar 

  8. D. Galic, and C. O. Horgan, J. Appl. Mech. 70, 426 (2003).

    Article  ADS  Google Scholar 

  9. W. Q. Chen, and K. Y. Lee, J. Strain Anal. Eng. Des. 39, 437 (2004).

    Article  Google Scholar 

  10. D. Guo, Z. Zheng, and F. Chu, Int. J. Solids Struct. 39, 725 (2002).

    Article  Google Scholar 

  11. S. Sun, D. Cao, and Q. Han, Int. J. Mech. Sci. 68, 180 (2013).

    Article  Google Scholar 

  12. S. Hosseini-Hashemi, M. R. Ilkhani, and M. Fadaee, Int. J. Mech. Sci. 76, 9 (2013).

    Article  Google Scholar 

  13. Y. H. Dong, Y. H. Li, D. Chen, and J. Yang, Compos. Part B-Eng. 145, 1 (2018).

    Article  Google Scholar 

  14. H. Y. Fang, J. S. Yang, and Q. Jiang, Int. J. Solids Struct. 39, 5241 (2002).

    Article  Google Scholar 

  15. P. Chadwick, C. F. M. Creasy, and V. G. Hart, J. Aust. Math. Soc. Ser. B Appl. Math. 20, 62 (1977).

    Article  Google Scholar 

  16. D. M. Haughton, and R. W. Ogden, J. Mech. Phys. Solids 28, 59 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  17. D. M. Haughton, and R. W. Ogden, Q. J. Mech. Appl. Math. 33, 251 (1980).

    Article  Google Scholar 

  18. J. Wang, A. Althobaiti, and Y. Fu, J. Mech. Mater. Struct. 12, 545 (2017).

    Article  MathSciNet  Google Scholar 

  19. A. Dorfmann, R. W. Ogden, and G. Saccomandi, Int. J. Solids Struct. 42, 3700 (2005).

    Article  Google Scholar 

  20. Y. Anani, and G. H. Rahimi, Int. J. Mech. Sci. 108–109, 122 (2016).

    Article  Google Scholar 

  21. F. Richard, A. Chakrabarti, B. Audoly, Y. Pomeau, and S. Mora, Proc. R. Soc. A 474, 20180242 (2018).

    Article  ADS  Google Scholar 

  22. S. Mora, Nonlin. Dyn. 100, 2089 (2020).

    Article  Google Scholar 

  23. A. Ertepinar, J. Sound Vib. 86, 343 (1983).

    Article  ADS  Google Scholar 

  24. A. Ertepinar, J. Sound Vib. 93, 457 (1984).

    Article  ADS  Google Scholar 

  25. D. M. Haughton, J. Sound Vib. 97, 107 (1984).

    Article  ADS  Google Scholar 

  26. A. Dorfmann, and R. W. Ogden, J. Elast. 82, 99 (2006).

    Article  Google Scholar 

  27. A. Dorfmann, and R. W. Ogden, IMA J. Appl. Math. 75, 603 (2010).

    Article  MathSciNet  Google Scholar 

  28. L. Dorfmann, and R. W. Ogden, Phil. Trans. R. Soc. A. 377, 20180077 (2019).

    Article  ADS  Google Scholar 

  29. B. Wu, Y. Su, W. Chen, and C. Zhang, J. Mech. Phys. Solids 99, 116 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  30. H. J. Ding, and W. Q. Chen, Three Dimensional Problems of Piezoelasticity (Nova Science Publishers, New York, 2001). p. 58.

    Google Scholar 

  31. W. Q. Chen, and H. J. Ding, The state-space method and its application in analyses of FGM structures, in Mechanics of Functionally Graded Materials and Structures, edited by Z. Zhong, L. Wu, and W. Q. Chen, (Nova Science Publishers, New York, 2012). pp. 139–178.

    Google Scholar 

  32. B. Wu, Y. Su, D. Liu, W. Chen, and C. Zhang, J. Sound Vib. 421, 17 (2018).

    Article  ADS  Google Scholar 

  33. C. Moler, and C. van Loan, SIAM Rev. 45, 3 (2003).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chaofeng Lü.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51988101, 11925206, and 11772295).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, K., Zhang, Y., Zhan, H. et al. Vibrational characteristics of rotating soft cylinders. Sci. China Phys. Mech. Astron. 64, 254611 (2021). https://doi.org/10.1007/s11433-020-1665-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-020-1665-9

PACS number(s)

Navigation