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
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References
- [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]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]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]S. H. Crandall. Non-gaussian closure techniques for stationary random vibration. Int. J. Non-Linear Mech., 20(1):1–8, 1985.MathSciNetMATHCrossRefGoogle Scholar
- [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]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]G. W. Housner. The behaviour of inverted pendulum structures during earthquakes. Bull Seism. Soc. America, 53(2):403–417, 1963.Google Scholar
- [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]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]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]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]N. C. Nigam. Introduction to Random Vibrations. MIT-Press, Cambridge MA., 1983.Google Scholar
- [13]J. B. Roberts and P. D. Spanos. Random Vibration and Statistical Linearization. J. Wiley & Sons, Chichester, 1990.MATHGoogle Scholar
- [14]T. T. Soong. Random Differential Equations in Science and Engineering. Academic Press, New York, 1973.MATHGoogle Scholar
- [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]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]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]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
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© Computational Mechanics Publications 1991