M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1964.
DOI : 10.1119/1.1972842

J. Auriault, Dynamic behaviour of a porous medium saturated by a newtonian fluid, International Journal of Engineering Science, vol.18, issue.6, pp.775-795, 1980.
DOI : 10.1016/0020-7225(80)90025-7

J. Auriault, L. Borne, and R. Chambon, Dynamics of porous saturated media, checking of the generalized law of Darcy, The Journal of the Acoustical Society of America, vol.77, issue.5, pp.1641-1650, 1985.
DOI : 10.1121/1.391962

J. Auriault, C. Boutin, and C. Geindreau, Homogenization of Coupled Phenomena in Heterogenous Media, 2009.
DOI : 10.1002/9780470612033

M. A. Biot, Theory of Propagation of Elastic Waves in a Fluid???Saturated Porous Solid. I. Low???Frequency Range, The Journal of the Acoustical Society of America, vol.28, issue.2, pp.168-191, 1956.
DOI : 10.1121/1.1908239
URL : https://hal.archives-ouvertes.fr/hal-01368668

J. P. Boehler, Application of Tensor Functions in Solid Mechanics, CISM Courses and Lectures, vol.292, 1987.
DOI : 10.1007/978-3-7091-2810-7

C. Boutin and J. L. Auriault, Dynamic behaviour of porous media saturated by a viscoelastic fluid. Application to bituminous concretes, International Journal of Engineering Science, vol.28, issue.11, pp.1157-1181, 1990.
DOI : 10.1016/0020-7225(90)90115-Y
URL : https://hal.archives-ouvertes.fr/hal-00936259

C. Boutin and C. Geindreau, Estimates and bounds of static and transient properties of granular and polyedra packing media, Phys. Rev. Lett. E, vol.82, issue.18, p.3613, 2010.

C. Boutin and J. Soubestre, Generalized inner bending continua for linear fiber reinforced materials, International Journal of Solids and Structures, vol.48, issue.3-4, pp.517-534, 2011.
DOI : 10.1016/j.ijsolstr.2010.10.017
URL : https://hal.archives-ouvertes.fr/hal-00941247

N. Buannic and P. Cartraud, Higher-order effective modeling of periodic heterogeneous beams. II. Derivation of the proper boundary conditions for the interior asymptotic solution, International Journal of Solids and Structures, vol.38, issue.40-41, pp.7168-7180, 2001.
DOI : 10.1016/S0020-7683(00)00423-6

D. L. Johnson, J. Koplik, and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, Journal of Fluid Mechanics, vol.24, issue.-1, pp.379-402, 1987.
DOI : 10.1121/1.388036

L. P. Li, K. Schulgasser, and G. Cederbaum, Theory of poroelastic beams with axial diffusion, Journal of the Mechanics and Physics of Solids, vol.43, issue.12, pp.2023-2042, 1995.
DOI : 10.1016/0022-5096(95)00056-O

G. Panasenko, Method of asymptotic partial decomposition of rod structures, Int. J. Comput. Civil Struct. Eng, vol.1, pp.57-70, 2000.

E. Sanchez-palencia, Non Homogeneous Media and Vibration Theory, 1980.

G. W. Scherer, Bending of gel beams: method for characterizing elastic properties and permeability, Journal of Non-Crystalline Solids, vol.142, pp.18-35, 1992.
DOI : 10.1016/S0022-3093(05)80003-1

G. W. Scherer, J. H. Prevost, and Z. H. Wang, Bending of a poroelastic beam with lateral diffusion, International Journal of Solids and Structures, vol.46, issue.18-19, pp.3451-3462, 2009.
DOI : 10.1016/j.ijsolstr.2009.05.016

M. R. Spiegel, Laplace transforms, Schaum Outline Series. Mc-Graw-Hill, 1965.

L. A. Taber, A Theory for Transverse Deflection of Poroelastic Plates, Journal of Applied Mechanics, vol.59, issue.3, p.628, 1992.
DOI : 10.1115/1.2893770

L. Trabucho and J. L. Viano, Mathematical modelling of rods, 1996.
DOI : 10.1016/S1570-8659(96)80006-8

D. Zhang and S. C. Cowin, Oscillatory bending of a poroelastic beam, Journal of the Mechanics and Physics of Solids, vol.42, issue.10, pp.1575-1599, 1994.
DOI : 10.1016/0022-5096(94)90088-4