Skip to main content
Log in

Localized response reductions in wide-band random vibration of uniform structures

  • Published:
Ingenieur-Archiv Aims and scope Submit manuscript

Summary

When a lightly damped uniform structure is excited by a broad band random source, there is a tendency for the mean-square velocity to be uniformly distributed over the structure as the number of responding modes increases. Localized zones or lanes of intensified response have been noted in one-dimensional and certain symmetrical two-dimensional structures. The present paper shows that under some circumstances there can also be localized zones or lanes of reduced response. The circumstances include asymmetric boundary conditions, excitation by a pair of sources with negative correlation, and excitation by a single source in a square structure with uniform boundary conditions when the source acts on the midline of the square.

Übersicht

Wenn eine wenig gedämpfte, gleichförmige Struktur durch breitbandige stochastische Kräfte angeregt wird, ergibt sich mit dem Ansteigen der Anzahl der angeregten Schwingungen, daß sich der Quadratmittelwert der Geschwindigkeiten gleichförmig über die Struktur verteilt. Es wurde früher gezeigt, daß in eindimensionalen und gewissen symmetrischen zweidimensionalen Strukturen intensivere Reaktionen in bestimmten Zonen oder Schneisen auftreten. In diesem Bericht wird gezeigt, daß sich in bestimmten Fällen auch Zonen oder Schneisen mit reduzierten Reaktionen ergeben. Diese Fälle umfassen solche mit asymmetrischen Randbedingungen, mit Anregungen durch zwei Kräfte mit negativer Korrelation, sowie die Anregung einer quadratischen Struktur mit gleichförmigen Randbedingungen durch eine Kraft, die auf der Mittellinie der Struktur angreift.

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. Crandall, S. H.; Wittig, L. E.: Chladni’s patterns for random vibrations of a plate. In: Herrmann, G.; Perrone, N. eds.): Dynamic Response of Structures, New York 1972, pp. 55–71

  2. Crandall, S. H.: Wide-band random vibrations of structures. 7th Proc. U.S. Nat. Congr. Appl. Mech., ASME, New York 1974, pp. 131–138

    Google Scholar 

  3. Young, L. E.: On the dynamic response of a damped membrane to a point stochastic load. M.I.T. Acoustics and Vibration Laboratory Rept. No. 81678-2, 1975

  4. Lee, S. S.: Lanes of intensified response in structures excited by wide-bond random excitation. Ph. D. Thesis, Dept. Mech. Engrng., M.I.T., Cambridge, Mass., 1976

    Google Scholar 

  5. Crandall, S. H.: Structured response patterns due to wide-band random excitation. In: Clarkson, B. L. (ed.): Stochastic Problems in Dynamics, London 1977, pp. 366–389

  6. Itao, K.; Crandall, S. H.: Wide-band random vibration of circular plates. J. Mech. Design 100 (1978) 690–695

    Google Scholar 

  7. Crandall, S. H.: Random vibration of one- and two-dimensional structures. In: Krishnaiah, P. R. (ed.): Developments in Statistics, Vol. 2, New York 1979, pp. 1–82

  8. Elishakoff, I.; Van Zanten, A. Th.; Crandall, S. H.: Wide band random axisymmetric vibration of cylindrical shells. J. Appl. Mechs. 46 (1979) 417–422

    Google Scholar 

  9. Langley, A. J.; Taylor, P. H.: Chladni patterns in random vibration. Int. J. Engrng Sci. 17 (1979) 1039 to 1047

    Google Scholar 

  10. Crandall, S. H.; Kulvets, A. P.: Source correlation effects on structural response. In: Krishnaiah, P. R. (ed.): Applications of Statistics, Amsterdam 1977, pp. 163–182

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Prof. Dr. Hans Ziegler on the occasion of his 70th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Crandall, S.H. Localized response reductions in wide-band random vibration of uniform structures. Ing. arch 49, 347–359 (1980). https://doi.org/10.1007/BF02426913

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02426913

Keywords

Navigation