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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
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).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01177401