Abstract
According to generalized characteristic theory, a characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media was performed. The characteristic differential equations and compatibility relations along bicharacteristics were deduced and the analytical expressions for wave surfaces were obtained. The characteristic and shapes of the velocity surfaces and wave surfaces in the transversely isotropic fluid-saturated porous media were discussed in detail. The results also show that the characteristic equations for stress waves in pure solids are particular cases of the characteristic equations for fluid-saturated porous media.
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References
Ting TCT. Characteristic forms of differential equations for wave propagation in nonlinear media [J].J Appl Mech, 1981,48(4):743–748.
Biot MA. Theory of propagation of elastic waves in a fluid-saturated porous solid—I: Low frequency range[J].J Acoust Soc Am, 1956,28(2):168–178.
Biot MA. Theory of propagation of elastic waves in a fluid-saturated porous solid—II: High frequency range[J].J Acoust Soc Am, 1956,28(2):179–191.
Biot MA. Mechanics of deformation and acoustic propagation in porous dissipative media[J].J Appl Phys, 1962,33(4):1482–1498.
Biot MA. Generalized theory of acoustic propagation in porous dissipative media[J].J Acoust Soc Am, 1962,34(9):1254–1264.
Plona TJ. Observation of a second bulk compressional wave in porous medium at ultrasonic frequencies[J].Appl Phys Lett, 1980,36(4):259–261.
Auriault JL, Borne L, Chambon R. Dynamics of porous saturated media, checking of the generalized law of Darcy[J].J Acoust Soc Am, 1985,77(5):1641–1950.
Johnson DL. Theory of dynamic permeability and tortuosity in fluid-saturated porous media[J].J Fluid Mech, 1987,176(3):379–402.
Schmitt PD. Acoustic multipole logging in transversely isotropic poroelastic formation[J].J Acoust Soc Am, 1989,86(6):2397–2421.
Sharma MD, Gogna ML. Wave propagation in anisotropic liquid-saturated porous solids[J].J Acoust Soc Am, 1991,90(2):1068–1073.
Liu Y, Liu K, Tanimura S. Wave propagation in transversely isotropic fluid-saturated poroelastic media[J].JSME International Journal, 2002,45(3):348–355.
Simon BR, Zienkiewicz OC, Paul DK. An analytical solution for the transversent response of saturated porous elastic solids[J].Intel J Numer Anal Mat, 1984,8(4):381–398.
José M Carcione. Wave propagation in anisotropic, saturated porous media: plane-wave theory and numerical simulation[J].J Acoust Soc Am, 1996,99(5):2665–2666.
TING Qi-cai.Nonlinear Waves in Solids[M]. Beijing: Chinese Friendship Publisher, 1985. (in Chinese).
Courant R, Hilbert D.Methods of Mathematical Physics, II [M]. New York: Wiley-Interscience, 1962.
Francis C Moon. Wave surfaces due to impact on anisotropic plates[J].J Compos Mater, 1972,6 (1):62–79.
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Communicated by HUANG Yong-nian
Foundation items: the National Natural Science Foundation of China (10232040, 10302002); the National Natural Science Foundation of China for Outstanding Young Scientists (10025212)
Biography: LIU Ying (1973 ≈), Doctor
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Ying, L., Kai-xin, L. Characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media. Appl Math Mech 25, 656–663 (2004). https://doi.org/10.1007/BF02438208
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DOI: https://doi.org/10.1007/BF02438208