Skip to main content

Parametric Instability and Process Identification

  • Conference paper
Analysis and Estimation of Stochastic Mechanical Systems

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 303))

Abstract

The topic of parametric instability and process identification is treated in two papers as follows.

  1. 1.

    Stability of Parametric Systems

  2. 2.

    Parameter Identification of Road Spectra and Nonlinear Oscillators

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Caughey, T.K.: Nonlinear theory of random vibrations, in: Advances in Applied Mechanics, 11, Academic Press, 1971, pp. 209–253.

    Google Scholar 

  2. Crandall, S.H.: Perturbation techniques for random vibrations of nonlinear systems. J. Acoustical Soc. Am., 35, 1963, pp. 1700–1705.

    Article  MathSciNet  Google Scholar 

  3. Wedig, W.: Regions of instability for a linear system with random parametric excitation, In: Lecture Notes in Math., 294, Springer-Verlag, New York, 1972, pp. 160–172.

    Google Scholar 

  4. Booton, R.C.: The analysis of nonlinear control systems with random inputs. IRE Trans. Circuit Theory, 1, 1954, pp. 32–34.

    Google Scholar 

  5. Caughey, T.K.: Equivalent linearization technique. J. Acoustical Soc. Am., 35, 1963, pp. 1706–1711.

    Article  MathSciNet  Google Scholar 

  6. Bogdanoff, J.L. and Kozim, F.: Moments of the output of linear random systems. J. Acoustical Soc. Am., 34, 1962, pp. 1063–1066.

    Article  Google Scholar 

  7. Wu, W.F. and Lin, Y.K.: Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations. Int. J. Non-linear Mech., 19, 1984, pp. 349–362.

    Article  MATH  MathSciNet  Google Scholar 

  8. Stratonovich, R.L.: Topics in the Theory of Random Noise, 1, Gordon and Breach, New York, 1963.

    Google Scholar 

  9. Ariaratnam, S.T.: Dynamic stability of a column under random loading, In: Pro. Int. Conf. on Dynamic Stability of Structures, Pergamon, New York, 1967, pp. 267.

    Google Scholar 

  10. Caughey, T.K.: Derivation and application of the Fokker-Planck equation, J. Acoust. Soc. Am., 35, 1963, p. 16–83.

    Google Scholar 

  11. Ito, K.: On a formula concerning stochastic differentials. Nagoya Math. J. Jap., 3, 1951, p. 55.

    MATH  Google Scholar 

  12. Parkus, H.: Random Processes in Mechanical Sciences, CISN Courses and Lectures, No 9, Springer-Verlag, Wien, 1969.

    Google Scholar 

  13. Wedig, W.: Stochastische Schwingungen — Simulation, Schatzung und Stabilität, ZAMM 67, 4, 1987, T34 - T42.

    MATH  MathSciNet  Google Scholar 

  14. Braun, H.: Spektrale Dichte von Fahrbahnunebenheiten. Tagungsband der VDI-Tagung Akustik und Schwingungstechnik, VDI-Verlag, Dusseldorf, 1970, pp. 539–546.

    Google Scholar 

  15. Magnus, W., Oberhettinger, F., Soni, R.P.: Formulas and Theorems for the Special Functions of Mathematical Physics, Springer-Verlag, Berlin, 1966, pp. 347–348.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Wien

About this paper

Cite this paper

Wedig, W.V. (1988). Parametric Instability and Process Identification. In: Schiehlen, W., Wedig, W. (eds) Analysis and Estimation of Stochastic Mechanical Systems. International Centre for Mechanical Sciences, vol 303. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2820-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2820-6_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82058-2

  • Online ISBN: 978-3-7091-2820-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics