Skip to main content

On the Generality of Systems Having an Infinitely Dense Discrete Spectrum of Resonant Frequencies

  • Conference paper
Refined Dynamical Theories of Beams, Plates and Shells and Their Applications

Part of the book series: Lecture Notes in Engineering ((LNENG,volume 28))

  • 341 Accesses

Abstract

The infinitely dense discrete spectrum of resonant frequencies has already been shown to exist in several “simple” systems such as strings and rods, Euler-Bernoulli beams and plates. Herein an attempt to prove the generality of this phenomenon will be presented. For that the more elaborate and accurate Timoshenko beam theory is adopted for formulation of the problem.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Shilkrut and Z. Grunseit “On systems having an infinitely dense discrete spectrum of resonant frequencies, ” Journal of Sound and Vibration, Vol. 100, No. 1, 1985, pp. 7–13.

    Article  ADS  Google Scholar 

  2. P.G. Kessel and A.L. Schlack, “Response of rods, strings and torsional members due to cyclic moving loads,” AIAA Journal, Vol. 4, 1966, pp. 1879–1880.

    Article  ADS  Google Scholar 

  3. T.F. Raske and A.L. Shlack, Jr., “Dynamic response of plates due to moving loads,” The Journal of the Acoustic Society of America, Vol. 42, No. 3, 1967, pp. 625–635.

    ADS  Google Scholar 

  4. G. Herrmann, “Forced motions of Timoshenko beams,” Journal of Applied Mechanics, Vol. 22, 1955, pp. 53–56.

    MATH  Google Scholar 

  5. C.L. Dolph, “On the Timoshenko theory of transverse beam vibrations,” Quarterly of Applied Mathematics, Vol. 12, 1954, pp. 175–187.

    MATH  MathSciNet  Google Scholar 

  6. Ya.S. Uflyand, “The propagation of waves in the transverse vibration of bars and plates,” Prikladnaia Mathematics i Mekhanica, Vol. 12, 1948, pp. 287–300 (in Russian).

    MathSciNet  Google Scholar 

  7. G.N. Watson A Treatise on the Theory of Bessel Functions 2nd ed. Cambridge University Press, 1966, pp. 22–23.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin, Heidelberg

About this paper

Cite this paper

Shilkrut, D., Grunseit, Z. (1987). On the Generality of Systems Having an Infinitely Dense Discrete Spectrum of Resonant Frequencies. In: Elishakoff, I., Irretier, H. (eds) Refined Dynamical Theories of Beams, Plates and Shells and Their Applications. Lecture Notes in Engineering, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83040-2_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-83040-2_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17573-5

  • Online ISBN: 978-3-642-83040-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics