Skip to main content

The spectrum of random vibration of a nonlinear oscillator

  • Conference paper
Applied Mechanics

Abstract

The study of random vibration deals with random excitation processes and the response of vibratory systems to such excitations. The most frequent application is to vehicles (e.g., ships, trucks, airplanes, space vehicles) where the operational environment provides random dynamic excitation (e.g., stormy seas, rough roads, atmospheric turbulence, rocket engine noise). For an introduction to the field see [1, 2]. A survey of the present state of the art is provided by [3].

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
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. Crandall, S. H.: Random Vibration. Appl. Mech. Rev. 12 (1959) 739–742.

    MathSciNet  Google Scholar 

  2. Crandall, S. H., and W. D. Mark: Random Vibration in Mechanical Systems. New York: Academic Press 1963.

    Google Scholar 

  3. Random Vibration, Vol. 2, edited by S. H. Crandall, Cambridge, Mass.: M.I.T. Press 1963.

    Google Scholar 

  4. Smith, P. W. jr.: Response of Nonlinear Structures to Random Excitation. J. Acoust. Soc. Am. 34 (1962) 827–835.

    Article  Google Scholar 

  5. Symposium on the Response of Nonlinear Systems to Random Excitation. J. Acoust. Soc. Am. 35 (1963) 1683-1721.

    Google Scholar 

  6. See p. 71 of [2].

    Google Scholar 

  7. Caughey, T. K.: Derivation and Application of the Fokker-Planck Equation to Discrete Nonlinear Dynamic Systems Subjected to White Random Excitation. J. Acoust. Soc. Am. 35 (1963) 1683–1692.

    Article  MathSciNet  Google Scholar 

  8. Khazen, E. M.: Estimating the Density of the Probability Distribution for Random Processes in Systems with Non-Linearities of Piecewise-Linear Type. Theory of Probability and its Applications 6 (1961) 214–220. Translation of Teoriya Veroyatuostei i ee Primeneniya 6 (1961) 234-242.

    Article  Google Scholar 

  9. Caughey, T. K., and J. K. Dienes: Analysis of a Nonlinear First-Order System with a White Noise Input. J. Appl. Phys. 32 (1961) 2476–2479.

    Article  MathSciNet  MATH  Google Scholar 

  10. Lyon, R. H.: The Random Vibration of Elastic Strings. WADC Technical Report 58-570, September 1958.

    Google Scholar 

  11. Crandall, S. H.: Perturbation Techniques for Random Vibration of Nonlinear Systems. J. Acoust. Soc. Am. 35 (1963) 1700–1705.

    Article  MathSciNet  Google Scholar 

  12. Shimogo, T.: Nonlinear Vibrations of Systems under Random Loading. Bull. J.S.M.E. 6 (1963) 44–52.

    Article  MathSciNet  Google Scholar 

  13. Shimogo, T.: Unsymmetrical Nonlinear Vibration Systems under Random Loading. Bull. J.S.M.E. 6 (1963) 53–59.

    Article  MathSciNet  Google Scholar 

  14. Crandall, S. H.: The Spectrum of Random Vibration of a Nonlinear Oscillator. AFOSR Technical Report, 64-1057, June 1964.

    Google Scholar 

  15. Caughey, T. K.: Equivalent Linearization Techniques. J. Acoust. Soc. Am. 35 (1963) 1706–1711.

    Article  MathSciNet  Google Scholar 

  16. Crandall, S. H.: Random Vibration of Systems with Nonlinear Restoring Forces, Proc. Int. Symp. on Nonlinear Vibrations, Vol. 1, pp. 306-314, Kiev 1963 (Trudy Mez. Simp. Nelineinym Kolebanijam).

    Google Scholar 

  17. Lyon, R. H.: Equivalent linearization of the hard spring oscillator. J. Acoust. Soc. Am. 32 (1960) 1161–1162.

    Article  Google Scholar 

  18. Butler, T. G.: Approximate Power Spectral Density of the Response of a Nonlinear System to Stationary Random Excitation. Martin Technical Note ER 12437, June 1962.

    Google Scholar 

  19. See Sec. 1.8 in [2].

    Google Scholar 

  20. Crandall, S. H.: Zero Crossings, Peaks, and Other Statistical Measures of Random Responses. J. Acoust. Soc. Am. 35 (1963) 1693–1699.

    Article  MathSciNet  Google Scholar 

  21. Timoshenko, S.: Vibration Problems in Engineering. 3rd Ed., Princeton, N. J.: D. van Nostrand Co. 1955, see p. 150.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1966 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Crandall, S.H. (1966). The spectrum of random vibration of a nonlinear oscillator. In: Görtler, H. (eds) Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-29364-5_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-29364-5_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-27863-5

  • Online ISBN: 978-3-662-29364-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics