Random Vibration of the Rigid Block

  • R. Giannini
  • R. Masiani

Abstract

The dynamic response of the rigid block oscillator to a Gaussian white noise excitation process is studied. The motion equation is linearized with the assumption of small displacements. The energy dissipation due to the inelastic impact is modeled as an impulsive process with arrivals occurring at displacement equal zero. The solution of the associated Fokker-Plank equation is obtained with two techniques of approximation: Gaussian closure and non-Gaussian closure. The non-Gaussian equations are written in terms of moments of arbitrary order, while the numerical application is limited to the fourth order.

Keywords

Seismic Response Random Vibration Rigid Block White Noise Process Duffing Oscillator 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Aslam, W. Godden, and D. T. Scalise. Earthquakes rocking response of rigid bodies. J. Struct Div. ASCE, 106(2):377–392, 1980.Google Scholar
  2. [2]
    C. Baggio, A. Giuffrè, and R. Masiani. Seismic response of masonry assemblages. In Proc. 9nd Europ. Conf. on Earthquake Eng., pages 221–230, Mosca, USSR, 1990.Google Scholar
  3. [3]
    S. H. Crandall. Non-gaussian closure for random vibration of non-linear oscillators. Int. J. Non-Linear Mech., 15:303–313, 1980.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    S. H. Crandall. Non-gaussian closure techniques for stationary random vibration. Int. J. Non-Linear Mech., 20(1):1–8, 1985.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    R. Giannini. Dynamic analysis of systems of staked blocks. In Proc. 2nd Nat. Conf. on Seismic Eng. in Italy, pages 47–62, Rapallo, Italy, 1984. (in Italian).Google Scholar
  6. [6]
    R. Giannini and R. Masiani. Frequency domain response of the rigid-block. In Proc. 10th Conf. AIMETA, pages 169–174, Pisa, Italy, 1990. (in Italian).Google Scholar
  7. [7]
    G. W. Housner. The behaviour of inverted pendulum structures during earthquakes. Bull Seism. Soc. America, 53(2):403–417, 1963.Google Scholar
  8. [8]
    R. N. Iyengar and P. K. Dash. Study of random vibration of nonlinear systems by gaussian closure technique. J. Appl. Mech. ASME, 45:393–399, 1978.MATHCrossRefGoogle Scholar
  9. [9]
    Y. K. Lin. Application of Markov processes theory to nonlinear random vibration problems. In Schueller and Shinozuka, editors, Stochastic Methods in Structural Dynamics, M. Nijhoff Publisher, 1987.Google Scholar
  10. [10]
    Q. Liu and H. G. Davies. Application of non-gaussian closure to the nonstationary response of a Duffing oscillator. Int. J. Non-Linear Mech., 23(3):241–250, 1988.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    K. Muto, H. Takase, K. Horikoshi, and H. Ueno. 3-D non linear dynamic analysis of staked blocks. In Proc. 2nd Special Conf. Dyn. Response Struct., pages 917–930, Atlanta, USA, 1981.Google Scholar
  12. [12]
    N. C. Nigam. Introduction to Random Vibrations. MIT-Press, Cambridge MA., 1983.Google Scholar
  13. [13]
    J. B. Roberts and P. D. Spanos. Random Vibration and Statistical Linearization. J. Wiley & Sons, Chichester, 1990.MATHGoogle Scholar
  14. [14]
    T. T. Soong. Random Differential Equations in Science and Engineering. Academic Press, New York, 1973.MATHGoogle Scholar
  15. [15]
    P. D. Spanos and A. S. Koh. Rocking of rigid blocks due to harmonic shaking. J. Eng. Mech. ASCE, 110(11):1627–1642, 1984.CrossRefGoogle Scholar
  16. [16]
    C. M. Wong and W. K. Tso. Steady state rocking response of rigid blocks part 2: experiment. Earth. Eng. Struct. Dyn., 18:107–120, 1989.CrossRefGoogle Scholar
  17. [17]
    W. F. Wu and Y. K. Lin. Cumulant neglect closure for non-linear oscillators under random parametric and external excitations. Int. J. Non-Linear Mech., 19(4):349–362, 1984.MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    C. S. Yim and J. Penzien A. K. Chopra. Rocking response of rigid blocks to earthquakes. Earth. Eng. Struct. Dyn., 8(6):565–587, 1980.CrossRefGoogle Scholar

Copyright information

© Computational Mechanics Publications 1991

Authors and Affiliations

  • R. Giannini
    • 1
  • R. Masiani
    • 2
  1. 1.Department of Engineering StructuresUniversity of L’AquilaItaly
  2. 2.Department of Structural and Geotechnical EngineeringUniversity of Rome “La Sapienza”Italy

Personalised recommendations