[1] |
Adomian, G. (1983): Stochastic systems. New York: Academic Press · Zbl 0523.60056 |
[2] |
Askar, A.; Cakmak, A. S. (1988): Seismic waves in random media. Prob. Eng. Mech. 3, 124-129 · doi:10.1016/0266-8920(88)90024-0 |
[3] |
Barucha-Reid, A. T. (1972): Random integral equations. New York: Academic Press |
[4] |
Bagtzoglou, A. C. (1990): Particle-grid methods with application to reacting flows and reliable solute source identification. Ph.D. dissertation, University of California, Irvine, California |
[5] |
Benaroya, H.; Rehak, M. (1987): The Neuman series/Born approximation applied to parametrically excited stochastic systems. Prob. Eng. Mech. 2, 74-81 · doi:10.1016/0266-8920(87)90018-X |
[6] |
Burczynski, T. (1985): The boundary element method for stochastic potential problems. Appl. Math. Mod. 9, 189-194 · Zbl 0586.60051 · doi:10.1016/0307-904X(85)90006-X |
[7] |
Chernov, L. A. (1962). Wave propagation in a random medium. New York: Dover |
[8] |
Chu, L.; Askar, A.; Cakmak, A. S. (1981): Earthquake waves in a, random medium. Int. J. Num. Anal. Meth. Geomech. 5, 79-96 · Zbl 0458.73086 · doi:10.1002/nag.1610050107 |
[9] |
Cruse, T. A.; Burnside, O. H.; Wu, Y. T.; Polch, E. Z.; Dias, I. B. (1988): Probabilistic structural analysis methods for select space propulsion system structural components (PSAM). Comput. Struct. 29, 891-901 · doi:10.1016/0045-7949(88)90356-2 |
[10] |
Dagan, G. (1989). Flow and transport in, porous formations, Berlin, Heidelberg, New York: Springer · Zbl 0673.76026 |
[11] |
Dias, J. B.; Nagtegaal, J. C. (1986): Efficient algorithms for use in probabilistic finite element analysis. In Burnside, O. H.; Parr, C. H. (eds) Advances in Aerospace Structural Analysis, Vol. AD-09, pp. 37-49, New York: ASME Publication |
[12] |
Drewniak, J. (1985): Research communication: boundary elements for random heat conduction problems. Eng. Anal. 2, 168-169 · doi:10.1016/0264-682X(85)90023-1 |
[13] |
Hoflord, R. L. (1981): Elementary source-type solutions of the reduced wave equation. J. Acoust. Soc. Am. 70, 1427-1436 · Zbl 0478.35030 · doi:10.1121/1.387099 |
[14] |
Hryniewicz, Z. (1991): Mean response to distributed dynamic loads across the random layer for anti-plane shear motion. Acta Mech. 90, 81-89 · Zbl 0749.73012 · doi:10.1007/BF01177401 |
[15] |
Ishimaru, A. (1978): Wave propagation, and scattering in random media, Vols. 1 and 2. New York: Academic Press · Zbl 0873.65115 |
[16] |
Karal, F. C.; Keller, J. B. (1964): Elastic, electromagnetic and other waves in a random medium. J. Math. Phys. 5, 537-549 · Zbl 0118.13302 · doi:10.1063/1.1704145 |
[17] |
Kohler, W.; Papanikolaou, G.; White, B. (1991): Reflection of waves generated by a point source over a randomly layered medium. Wave Motion 13, 53-87 · Zbl 0735.73021 · doi:10.1016/0165-2125(91)90005-9 |
[18] |
Kotulski, Z. (1990): Elastic waves in randomly stratified medium. Analytical results. Acta Mech. 83, 61-75 · Zbl 0721.73009 · doi:10.1007/BF01174733 |
[19] |
Lafe, O. E.; Cheng, A. H. D.: (1987) A perturbation boundary element code for steady-state groundwater flow in heterogeneous aquifers. Water Resour. Res. 23, 1079-1084 · doi:10.1029/WR023i006p01079 |
[20] |
Li, Y. L.; Liu, C. H.; Franke, S. J. (1990): Three-dimensional Green’s function for wave propagation in a linearly inhomogeneous medium?the exact analytic solution. J. Acoust. Soc. Am. 87, 2285-2291 · doi:10.1121/1.399072 |
[21] |
Liu, K. C. (1991): Wave scattering in discrete random media by the discontinuous stochastic field method I: Basic method and general theory. J. Sound Vibr. 147, 301-311 · doi:10.1016/0022-460X(91)90717-X |
[22] |
Liu, W. K.; Belytschko, T.; Mani, A. (1986): Random field finite elements. Int. J. Num. Meth. Eng. 23, 1831-1845 · Zbl 0597.73075 · doi:10.1002/nme.1620231004 |
[23] |
Luco, J. E.; Wong, H. L. (1986): Response of a rigid foundation to a spatially random ground motion. Earthquake Eng. Struct. Dyn. 14, 891-908 · doi:10.1002/eqe.4290140606 |
[24] |
Manolis, G. D.; Beskos, D. E. (1988): Boundary element methods in elastodynamics. London: Chapman and Hall |
[25] |
Manolis, G. D.; Shaw, R. P. (1990): Random wave propagation using boundary elements. In: Tanaka, M.; Brebbia, C. A.; Shaw, R. P. (eds). Advances in boundary element methods in Japan and USA, Topics in Engineering, Vol. 7. Southampton: Computational Mechanics Publications |
[26] |
Manolis, G. D.; Shaw, R. P. (1992): Wave motion in a random hydroacoustic medium using boundary integral/element methods. Eng. Anal. Bound. Elem 9, 61-70 · doi:10.1016/0955-7997(92)90125-Q |
[27] |
McLachlan, N. W. (1954). Bessel functions for engineers. Oxford: Clarendon Press · JFM 61.1177.05 |
[28] |
Mindlin, R. D. (1936): Force at a point in the interior of a semi-infinite solid. J. Phys. 7, 195-202 · JFM 62.1531.03 · doi:10.1063/1.1745385 |
[29] |
Pai, D. M. (1991): Wave propagation in inhomogeneous media: a planewave layer interaction method. Wave Motion 13, 205-209 · doi:10.1016/0165-2125(91)90058-V |
[30] |
Pais, A. L.; Kausel, E. (1990): Stochastic response of rigid foundations. Earthquake Eng. Struct. Dyn. 19, 611-622 · doi:10.1002/eqe.4290190411 |
[31] |
Pekeris, C. L. (1946): Theory of propagation of sound in a half-space of variable sound velocity under conditions of formation of a sound zone. J. Acoust Soc. Am. 18, 295-315 · Zbl 0063.06149 · doi:10.1121/1.1916366 |
[32] |
Shaw, R. P. (1991): Boundary integral equations for nonlinear problems by the Kirchhoff transformation. In: Brebbia, C. A.; Gipson, G. S. (eds): Boundary Elements XIII, pp. 59-69. London: Elsevier |
[33] |
Shaw, R. P.; Makris, N. (1991) Green’s functions for Helmholtz and Laplace equations in heterogeneous media. In: Brebbia, C. A.; Gipson, G. S. (eds): Boundary Elements XIII, pp. 59-69. London: Elsevier |
[34] |
Shinozuka, M. (1972) Digital simulation of random processes and its applications. J. Sound Vibr 25, 111-128 · doi:10.1016/0022-460X(72)90600-1 |
[35] |
Spanos, P. D.; Ghanem, R. (1991): Boundary element formulation for random vibration problems. J. Eng. Mech. ASCE 117, 409-423 · doi:10.1061/(ASCE)0733-9399(1991)117:2(409) |
[36] |
Sobczyk, K. (1976): Elastic wave propagation in a discrete random medium. Acta Mech. 25, 13-28 · Zbl 0351.73034 · doi:10.1007/BF01176926 |
[37] |
Varadan, V. K.; Ma, Y.; Varadan, V. V. 1985): Multiple scattering theory for elastic wave propagation in discrete random media. J. Acous. Soc. Am. 77, 375-389 · Zbl 0574.73040 · doi:10.1121/1.391910 |
[38] |
Vanmarke, E.; Shinozuka, M.; Nakagiri, S.; Schueller, G. I.; Grigoriu, M. (1986): Random fields and stochastic finite elements. Struct. Safety 3, 143-166 · doi:10.1016/0167-4730(86)90002-0 |
[39] |
Vrettos, C. (1990a): Dispersive SH-surface waves in soil deposits of variable shear modulus. Soil Dyn. Earthquake Eng. 9, 255-264 · doi:10.1016/S0267-7261(05)80004-1 |
[40] |
Vrettos, C. (1990b): In-plane vibrations of soil deposits with variable shear modulus: I. Surface waves, and II. Line load. Int. J. Num. Anal. Meth. Geomech. 14, 209-222 and 649-662 · Zbl 0702.73051 · doi:10.1002/nag.1610140304 |
[41] |
Brettos, C. (1991a). Forced anti-plane vibrations at the surface of an inhomogeneous half-space. Soil Dyn. Earthquake Eng. 10, 230-235 · doi:10.1016/0267-7261(91)90016-S |
[42] |
Vrettos, C. (1991b): Time-harmonic Boussinesq problem for a continuously non-homogeneous soil. Earthquake Eng. Struct. Dyn. 20, 961-977 · doi:10.1002/eqe.4290201006 |