Summary
The mean field equation for SH-waves in a random medium, for the distributed linearly varying dynamic load acting across the thickness of the layer, is obtained. Assuming local independence assumption of Bourret, a closed form solution for average displacements and stresses for two-layered viscoelastic half-space is derived. The dimensionless average influence functions, found in this paper, may be used in solving the dynamic soil-structure interaction problems by the boundary element method.
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References
Wolf, J. P.: Dynamic soil-structure interaction. New York: Prentice Hall 1985.
Frankel, A., Clayton, R. W.: Finite difference simulations of seismic scattering implications for the propagation of short-period seismic waves in the crust and models of crustal heterogeneity. J. Geophys. Res.91 (B6), 6465–6489 (1986).
McCoy, J. J.: Macroscopic response of continua with random microstructures. Mechanics today6 (Nemat-Nasser, S., ed.), pp. 1–40. Pergamon Press 1981.
Bourret, R. C.: Stochastically perturbed fields with applications to wave propagation in random media. Nuovo Cimento26, 1–31 (1962).
Bourret, R. C.: Propagation of random perturbed fields. Canadian J. Phys.40, 782–790 (1962).
Richardson, J. M.: The application of truncated hierarchy techniques in the solution of a stochastic linear differential equation. Proc. Symp. Appl. Math., Am. Math. Soc.16, 290–302 (1964).
Soong, T. T.: Random differential equations in science and engineering. New York: Academic Press 1973.
Hryniewicz, Z., Hermans, A. J.: Free-field response from inclined body waves in a viscoelastic random medium. Earthq. Engrg. and Struct. Dyn.18, 1025–1040 (1989).
Vanmarcke, E.: Random fields, analysis and synthesis. London: The M.I.T. Press 1988.
Kawano, M., Kobori, T.: Characteristics of earthquake ground motion propagating through the medium with random geological properties. Trans. A. I. J.330, 66–77 (1983) (in Japanese).
Karal, F. C., Keller, J. B.: Elastic, electromagnetic and other waves in a random medium. J. Math. Phys.5 (4), 537–547 (1964).
Adomian, G.: Stochastic systems. New York: Academic Press 1983.
Baker, R., Zeitoun, D. G.: Application of Adomian's decomposition procedure to the analysis of a beam on random Winkler support. Int. J. Solids Structures26 (2), 217–235 (1990).
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Hryniewicz, Z. Mean response to distributed dynamic load across the random layer for anti-plane shear motion. Acta Mechanica 90, 81–89 (1991). https://doi.org/10.1007/BF01177401
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DOI: https://doi.org/10.1007/BF01177401