Summary
The governing equations of flexural vibrations of thin, fluid-saturated poroelastic plates are derived in detail. The plate material obeys Biot's theory of poroelasticity with one degree of porosity, while the plate theory employed is the one due to Kirchhoff. These governing equations are compared with the corresponding ones for thermoelastic plates and a poroelastic-thermoelastic analogy for flexural plate dynamics is established in the frequency domain. The dynamic response of a rectangular, simply supported, poroelastic plate to harmonic load is obtained analytically-numerically and the effects of inertia as well as of porosity and permeability on the response is assessed.
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Biot, M. A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. Part I. Low-frequency range. J. Acoust. Soc. Am.28, 168–178 (1956).
Vardoulakis, I., Beskos, D. E.: Dynamic behavior of nearly saturated porous media. Mech. Mat.5, 87–108 (1986).
Corapcioglu, M. Y.: Wave propagation in porous media—a review. In: Transport processes in porous media (Bear, J., Corapcioglou, M. Y., eds.), pp. 373–469, Dordrecht: Kluwer Academic Publishers 1991.
Deresiewicz, H.: The effect of boundaries on wave propagation in a liquid-filled porous solid. Part I. Reflection of plane waves at a free plane boundary (non-dissipative case). Bull. Seismol. Soc. Am.50, 599–607 (1960).
Deresiewicz, H.: The effect of boundaries on wave propagation in a liquid-filled porous solid. Part IV. Surface waves in a half-space. Bull. Seismol. Soc. Am.52, 627–638 (1962).
Deresiewicz, H., Rice, T.: The effect of boundaries on wave propagation in a liquid-filled porous solid. Part III. Reflection of plane waves at free plane boundary (general case). Bull. Seismol. Soc. Am.52, 595–625 (1962).
Ghaboussi, J., Wilson, E. L.: Variational formulation of dynamics of fluid-saturated porous elastic solids. J. Engng. Mech. Div. ASCE98, 947–963 (1972).
Garg, S. K., Nayfeh, A. H., Good, A. J.: Compressional waves in fluid-saturated elastic porous media. J. Appl. Phys.45, 1968–1974 (1974).
Zienkiewicz, O. C., Chang, C. T., Bettess, P.: Drained, undrained, consolidating and dynamic behavior assumptions in soils. Geotechnique30, 385–395 (1980).
Zienkiewicz, O. C., Shiomi, T.: Dynamic behavior of saturated porous media: the generalized Biot formulation and its numerical solution. Int. J. Numer. Anal. Meth. Geomech.8, 71–96 (1984).
Mei, C. C., Foda, M. A.: Wave-induced response in a fluid filled poro-elastic solid with a free surface. Geophys. J. Roy. Astronom. Soc.66, 597–631 (1981).
Mei, C. C., Si, B. I., Cai, D.: Scattering of simple harmonic waves by a circular cavity in a fluid-infiltrated poro-elastic medium. Wave Motion6, 265–278 (1984).
Gazetas, G., Petrakis, E.: Offshore caissons on porous saturated soil. In: Proceedings of international conference on recent advances in geotechnical earthquake engineering and soil dynamics (Prakash, S. ed.), pp. 381–386. Rolla: University of Missouri-Rolla 1981.
Verruijt, A.: Approximations of cyclic pore pressures caused by sea waves in a poro-elastic half-plane. In: Soil mechanics-transient and cyclic loads (Pande, G. N., Zienkiewicz, O. C., eds.), pp. 37–51. New York: Wiley 1982.
Prevost, J. H.: Nonlinear transient phenomena in saturated porous media. Comp. Meth. Appl. Mech. Engng.30, 3–18 (1982).
Prevost, J. H.: Wave propagation in fluid-saturated porous media: an efficient finite element procedure. Soil Dyn. Earthquake Engng.4, 183–202 (1985).
Bowen, R. M., Lockett, R. R.: Inertial effects in poroelasticity. J. Appl. Mech. ASME50, 334–342 (1983).
Halpern, M., Christiano, P.: Steady-state harmonic response of a rigid plate bearing on a liquidsaturated poroelastic half space. Earthquake Engng. Struct. Dyn.14, 439–454 (1986).
Hiremath, M. S., Sandhu, R. S., Morland, L. W., Wolfe, W. E.: Analysis of one-dimensional wave propagation in a fluid-saturated finite soil column. Int. J. Numer. Anal. Meth. Geomech.12, 121–139 (1988).
Cheng, A. H. D., Badmus, T., Beskos, D. E.: Integral equation for dynamic poroelasticity in frequency domain with BEM solution. J. Engng. Mech. ASCE117, 1136–1157 (1991).
Vgenopoulou, I., Beskos, D. E.: Dynamic poroelastic soil column and borehole problem analysis. Soil Dyn. Earthquake Engng.11, 335–345 (1992).
Biot, M. A.: Theory of buckling of a porous slab and its thermoelastic analogy. J. Appl. Mech. ASME31, 194–198 (1964).
Nowinski, J. L., Davis, C. F.: The flexure and torsion of bones viewed as anisotropic poroelastic bodies. Int. J. Eng. Sci.10, 1063–1079 (1972).
Nowacki, W.: Dynamic problems of thermoelasticity. Leyden: Nordhoff 1975.
Biot, M. A., Willis, D. G.: The elastic coefficients of the theory of consolidation. J. Appl. Mech. ASME24, 594–601 (1957).
Szilard, R.: Theory and analysis of plates. Englewood Cliffs: Prentice Hall 1974.
Fatt, I.: The Biot-Willis coefficients for a sandstone. J. Appl. Mech. ASME26, 296–297 (1959).
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Theodorakopoulos, D.D., Beskos, D.E. Flexural vibrations of poroelastic plates. Acta Mechanica 103, 191–203 (1994). https://doi.org/10.1007/BF01180226
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DOI: https://doi.org/10.1007/BF01180226