Advertisement

Ingenieur-Archiv

, Volume 45, Issue 5–6, pp 361–370 | Cite as

Biaxial slip of a mass on a foundation subjected to earthquake motions

  • S. H. Crandall
  • S. S. Lee
Article

Summary

The relative motion of a rigid mass on a horizontal foundation undergoing biaxial random motion in the horizontal plane is studied under the assumption that Coulomb friction acts between the mass and the foundation. The displacement of the mass with respect to the foundation is a two-dimensional random walk whose statistical parameters depend nonlinearly on the intensity and correlation of the biaxial excitation. Analytical results are obtained via the Fokker-Planck equation and the Equivalent Linearization procedure and simulation results are obtained via the digital computer. These results may be useful for predicting the accumulated slip of a stiff compact structure free to slide on its foundation during an earthquake.

Keywords

Relative Velocity Coulomb Friction Earthquake Motion Vector Relative Velocity Rigid Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Übersicht

Die relativen Bewegungen zwischen einer starren Masse auf einem horizontalen Fundament, das biaxalen wahllosen Bewegungen unterworfen ist, werden unter der Annahme studiert, daß zwischen der Masse und dem Fundament Coulomb-Reibung herrscht. Die Verschiebung der Masse relativ zum Fundament ist eine zweidimensionale wahllose Bahn, deren statistische Parameter in nichtlinearer Weise von der Intensität und der Wechselbeziehung zwischen den biaxialen Erregungen abhängen. Mit Hilfe der Fokker-Planck-Gleichung und der äquivalenten Linearisierung werden analytische Resultate erhalten, während Simulations-Ergebnisse über einen Digitalrechner gewonnen werden. Diese Resultate können wichtig sein, um das Gleiten einer starren Struktur, die sich mit Coulomb-Reibung aber sonst uneingeschränkt auf ihrem Fundament bewegen kann, während eines Erdbebens zu berechnen.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Williams, J. H., Jr.: Designing Earthquake-Resistant Structures. Technology Review 76 (1973) pp. 37–43Google Scholar
  2. 2.
    Crandall, S. H.; Lee, S. S.; Williams J. H.; Jr.: Accumulated Slip of a Friction-Controlled Mass Excited by Earthquake Motions. J. Appl. Mech. 41, (1974) pp. 1094–1098Google Scholar
  3. 3.
    Lee, S. S.: Accumulated Slip of a Continuous Structure Driven by Friction under Earthquake Excitation. Acoustics and Vibration Laboratory Report, No. 80463-1, Massachusetts Institute of Technology, Cambridge, Mass., May, 1974.Google Scholar
  4. 4.
    Klotter, K.: The Attenuation of Damped Free Vibrations and the Derivation of the Damping Law from Recorded Data. Proc. 2nd U.S. National Congress of Applied Mechanics, ASME, N.Y., 1954, pp. 85–93Google Scholar
  5. 5.
    Klotter, K.: An extension of the Conventional Concept of the Describing Function. Proc. Symposium on Nonlinear Circuit Analysis, Polytechnic Institute of Broklyn, N.Y., 1953Google Scholar
  6. 6.
    Caughey, T. K.: Derivation and Application of the Fokker-Planck Equation to Discrete Nonlinear Dynamic Systems Subjected to White Random Excitation. J. Acoust. Soc. Amer. 35, (1963) pp. 1683–1692MathSciNetCrossRefGoogle Scholar
  7. 7.
    Milne-Thomson, L. M.: Jacobian Elliptic Function Tables. New York 1950Google Scholar
  8. 8.
    Caughey, T. K.: Equivalent Linearization Techniques. J. Acoust. Soc. Amer. 35 (1963) pp. 1706–1711MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lin, Y. K.: Probabilistic Theory of Structural Dynamics, Chapter 6, New York 1967.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • S. H. Crandall
    • 1
  • S. S. Lee
    • 1
  1. 1.Massachusetts Institute of Technology, Dept. of Mechanical EngineringCambridgeUSA

Personalised recommendations