Uniaxial waves in randomly heterogeneous elastic media

Probabilistic Engineering Mechanics

Volumn 13, Issue 1, 1998, Pages 27-38

  Belyaev, Alexander K ^a   Ziegler, Franz ^b  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ATTENUATION; CORRELATION METHODS; DIFFERENTIAL EQUATIONS; ELASTICITY; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; RANDOM PROCESSES;

CORRELATION FUNCTIONS; DYSON INTEGRAL EQUATION; LIOUVILLE SUBSTITUTION; RANDOMLY HETEROGENEOUS ELASTIC MEDIA; UNIAXIAL SOUND WAVES;

ACOUSTIC WAVE TRANSMISSION;

EID: 0031675352     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0266-8920(97)00005-2     Document Type: Article

References (22)

1. Kröner, E., Statistical modelling. Modelling small deformations of polycrystals, ed. J. Gittus and J. Zarka. Elsevier Applied Science, London, 1986, pp. 229-291.
2. Tatarsky, V. I., Wave Propagation in Turbulent Atmosphere (in Russian). Nauka, Moscow, 1969.
3. Ibrahim, R. A., Structural dynamics with parameter uncertainties. Applied Mechanics Review, 1987, 40, 309-328.
4. Roseau, M., Asymptotic Wave Theory. North-Holland, Amsterdam, 1976.
5. Karal, F. C. and Keller, J. B., Elastic, electro-magnetic and other waves in a random medium. J. Mathematical Physics, 1964, 5, 537-547.
6. Sobczyk, K., Stochastic Wave Propagation. Elsevier, Amsterdam, 1985.
7. Makarov, B. P., Nonlinear Problems of Statistical Dynamics of Machines and Devices (in Russian). Mashinostroenie, Moscow, 1983.
8. Náprstek, J., Dispersion of longitudinal waves propagating in a continuum with randomly perturbated parameters. Proc. 3rd Int. Conf. on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, ed. S. Prakash, University of Missouri Rolla, St. Louis, 1995, pp. 705-708.
9. Náprstek, J., Propagation of longitudinal stochastic waves in bars with random parameters. Structural Dynamics, ed. G. Augusti, C. Borri and P. Spinelli. A. A. Balkema, Rotterdam, 1996, pp. 51-60.
10. Ziegler, F., Random vibrations: A spectral method for linear and nonlinear structures. Probabilistic Engineering Mechanics, 1987, 2, 92-99.
11. Heading, J., An Introduction to Phase-integral Methods. Wiley, New York, 1962.
12. Lin, Y. K., Probabilistic Theory of Structural Dynamics. McGraw-Hill, New York, 1967.
13. Soong, T. T., Random Differential Equations. Academic Press, 1973, pp. 239-243.
14. Rieder, G., Iterationsverfahren und Operatorgleichungen in der Elastizitätstheorie. Abh. Braunschweig. Wiss. Ges., 1962, 14, 109-155.
15. Kröner, E., Elastic moduli of perfectly disordered composite materials. J. Mechanics & Physics of Solids, 1967, 15, 319-327.
16. Eimer, C., Stresses in multi-phase media. Arch. Mech. Stos., 1967, 19, 521-538.
17. Frisch, U., Wave propagation in continuous random media. Probabilistic Methods in Applied Mathematics, ed. A. T. Bharucha-Reid. Academic Press, New York, 1968, pp. 128-159.
18. Gambin, E. and Kröner, E., Convergence problems in the theory of random elastic media. J. Engineering Science, 1981, 19, 313-329.
19. Brillouin, L., Wave Propagation in Periodic Structures. Dover Publications, New York, 1953.
20. Ziegler, F., Mean waves in laminated random media. Int. J. Solids and Structures, 1969, 5, 893-914.
21. Chen, K. K. and Soong, T. T., Covariance properties of waves propagating in a random medium. J. Acoustical Society America, 1971, 49, 1639-1642.
22. McCoy, J. J., On the correlation of field quantities in a random linearly elastic solid. J. Mathematical Physics, 1972, 13, 1804-1814.