Skip to main content

Pinned-Pinned Columns under a Pulsating Axial Force

  • Chapter
  • First Online:
Dynamic Stability of Columns under Nonconservative Forces

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 255))

Abstract

There are many examples of physical systems, including structural systems, that are subject to time-varying excitations. One example is a string subjected to a pulsating axial tension. The string loses its stability by so-called parametric resonance , which occurs primarily when the excitation frequency \( \theta \) is twice the string’s eigenfrequency \( \omega_{\text{o}} \), that is, \( \theta = 2\omega_{\text{o}} \).

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Melde, F. (1860). Über die Erregung stehender Wellen eines fadenförmigen Körpers. Annalen der Physik und Chemie, 109, 193–215.

    Article  Google Scholar 

  2. Rayleigh, J. W. S. (1945). The Theory of Sound (Vol. I). New York: Dover Publications, Inc.

    MATH  Google Scholar 

  3. Bolotin, V. V. (1964). The dynamic stability of elastic systems. San Francisco: Holden-Day Inc.

    MATH  Google Scholar 

  4. Beliaev, N. M. (1924). Stability of prismatic rods subjected to variable longitudinal forces. In Collection of Papers; Engineering Constructions and Structural Mechanics, Leningrad (p. 149, in Russian).

    Google Scholar 

  5. Nishino, K. (1939). Vibrational stability of a bar under periodic longitudinal forces. Journal of the Aeronautical Research Institute, Tokyo Imperial University, 176, p. 93 (in Japanese).

    Google Scholar 

  6. Sugiyama, Y., Iwatsubo, T., & Ishihara, K. (1972). On nonsteady-state motions in the vicinity of the boundaries of the principal region of dynamic instability. Report of the Faculty of Engineering, Tottori University, 2(2), 28–37.

    Google Scholar 

  7. Somerset, J. H., & Evan-Iwanowski, R. M. (1964). Experiments on parametric instability of columns, development of theoretical and applied mechanics. In South-Eastern Conference on Theoretical and Applied Mechanics.

    Google Scholar 

  8. Evan-Iwanowski, R. M. (1965). On the parametric response of structures. Applied Mechanics Review, 18(9), p. 699.

    Google Scholar 

  9. Sugiyama, Y., Kawagoe, H., & Iwatsubo, T. (1972). On instability criteria in digital simulation of parametric instability. Reports of the Faculty of Engineering, Tottori University, 3(1), 1–9.

    Google Scholar 

  10. Iwatsubo, T., Sugiyama, Y., & Ishihara, K. (1972). Stability and non-stationary vibration of columns under periodic loads. Journal of Sound and Vibration, 23(2), 245–257.

    Article  Google Scholar 

  11. Song, Z., Chen, Z., Li, W., & Chai, Y. (2016). Parametric instability analysis of a rotating shaft subjected to a periodic axial force by using discrete singular convolution method. Meccanica, 51(6), 1–15.

    MATH  Google Scholar 

  12. Huang, Y., Liu, A., Pi, Y., Lu, H., & Gao, W. (2017). Assessment of lateral dynamic instability of columns under an arbitrary axial load owing to parametric resonance. Journal of Sound and Vibration, 395, 272–293.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yoshihiko Sugiyama .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sugiyama, Y., Langthjem, M.A., Katayama, K. (2019). Pinned-Pinned Columns under a Pulsating Axial Force. In: Dynamic Stability of Columns under Nonconservative Forces. Solid Mechanics and Its Applications, vol 255. Springer, Cham. https://doi.org/10.1007/978-3-030-00572-6_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-00572-6_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00571-9

  • Online ISBN: 978-3-030-00572-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics