Vibration Analysis of an Infinite Poroelastic Circular Cylindrical Shell Immersed in Fluid

Syed Ahmed Shah

Department of Mathematics, Deccan College of Engineering and Technology, Hyderabad, India.

DOI: 10.4236/oja.2012.22010                

Abstract

The purpose of this paper is to study the effect of presence of fluid within and around a poroelastic circular cylindrical shell of infinite extent on axially symmetric vibrations. The frequency equation each for a pervious and an impervious surface is obtained employing Biot’s theory. Radial vibrations and axially symmetric shear vibrations are uncoupled when the wavenumber is vanished. The propagation of axially symmetric shear vibrations is independent of presence of fluid within and around the poroelastic cylindrical shell while the radial vibrations are affected by the presence of fluid. The frequencies of radial vibrations and axially symmetric shear vibrations are the cut-off frequencies for the coupled motion of axially symmetric vibrations. The non-dimensional phase velocity as a function of ratio of thickness to wavelength is computed and presented graphically for two different types of poroelastic materials for thin poroelastic shell, thick poroelastic shell and poroelastic solid cylinder.

Keywords

Biot’s Theory; Axially Symmetric Vibrations; Radial Vibrations; Poroelastic Cylindrical Shell; Pervious Surface; Impervious Surface; Phase Velocity; Cut-off Frequency

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. C. Gazis, “Three Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinders,” Journal of the Acoustical Society of America, Vol. 31, 1959, pp. 568-587. doi:10.1121/1.1907753
[2]	L. Bjorno and R. Kumar, “Fluid Influenced Stress Wave Dispersion in Submerged Rods,” Acustica, Vol. 27, 1972, pp. 329-334.
[3]	J. Chandra, R. Kumar and Y. K. Mehta, “Dispersion of Axially Symmetric Waves in Cylindrical Shells Immersed in an Acoustic Medium,” Acustica, Vol. 35, 1976, pp. 1-10.
[4]	M. A. Biot, “Theory of Propagation of Elastic Waves in Fluid Saturated Porous Solid,” Journal of the Acoustical Society of America, Vol. 28, No. 2, 1956, pp. 168-178. doi:10.1121/1.1908239
[5]	M. Tajuddin and K. S. Sarma, “Torsional Vibrations of Poroelastic Cylinders,” Journal of Applied Mechanics, Vol. 47, 1980, pp. 214-216.
[6]	C. J. Wisse, D. M. J. Smeulders, M. E. H. van Dongen and G. Chao, “Guided Wave Modes in Porous Cylinders: Experimental Results,” Journal of the Acoustical Society of America, Vol. 112, No. 3, 2002, pp. 890-895. doi:10.1121/1.1497621
[7]	C. J. Wisse, D. M. J. Smeulders, G. Chao and M. E. H. van Dongen, “Guided Wave Modes in Porous Cylinders: Theory,” Journal of the Acoustical Society of America, Vol. 122, No. 4, 2007, pp. 2049-2056. doi:10.1121/1.2767418
[8]	G. Chao, D. M. J. Smeulders and M. E. H. van Dongen, “Shock-Induced Borehole Waves in Porous Formations: Theory and Experiments,” Journal of the Acoustical Society of America, Vol. 116, No. 2, 2004, pp. 693-702. doi:10.1121/1.1765197
[9]	A. K. Vashishth and P. Khurana, “Wave Propagation along a Cylindrical Borehole in an Anistropic Poroelastic Solid,” Geophysical Journal International, Vol. 161, No. 3, 2005, pp. 295-302. doi:10.1111/j.1365-246X.2005.02540.x
[10]	H. Farhang, E. Esmaeil, N. S. Anthony and A. Mirnezami, “Wave Propagation in Transversely Isotropic Cylinders,” International Journal of Solids and Structures, Vol. 44. No. 16, 2007, pp. 5236-5246. doi:10.1016/j.ijsolstr.2006.12.029
[11]	M. Tajuddin and S. Ahmed Shah, “Circumferential Waves of Infinite Hollow Poroelastic Cylinders,” Journal of Applied Mechanics, Vol. 73, No. 4, 2006, pp. 705-708. doi:10.1115/1.2164513
[12]	M. Tajuddin and S. Ahmed Shah, “On Torsional Vibrations of Infinite Hollow Poroelastic Cylinder,” Journal of Mechanics of Materials and Structures, Vol. 2, No. 1, 2007, pp. 189-200. doi:10.2140/jomms.2007.2.189
[13]	S. Ahmed Shah, “Axially Symmetric Vibrations of Fluid Filled Poroelastic Circular Cylindrical Shells,” Journal of Sound and Vibration, Vol. 318, No. 1-2, 2008, pp. 389-405. doi:10.1016/j.jsv.2008.04.012
[14]	S. Ahmed Shah and M. Tajuddin, “On Axially Symmetric Vibrations Fluid Filled Poroelastic Spherical Shells,” Open Journal of Acoustics, Vol. 1, No. 2, 2011, pp. 15-26. doi:10.4236/oja.2011.12003
[15]	I. Fatt, “The Biot-Willis Elastic Coefficients for a Sandstone,” Journal of Applied Mechanics, Vol. 26, 1959, pp. 296-297.
[16]	C. H. Yew and P. N. Jogi, “Study of Wave Motions in Fluid-Saturated Porous Rocks,” Journal of the Acoustical Society of America, Vol. 60, 1976, pp. 2-8. doi:10.1121/1.381045