On Axially Symmetric Vibrations of Fluid Filled Poroelastic Spherical Shells

Syed Ahmed  Shah; Mohammed  Tajuddin

doi:10.4236/oja.2011.12003

Syed Ahmed Shah, Mohammed Tajuddin

Abstract: Employing Biot’s theory of wave propagation in liquid saturated porous media, waves propagating in a hollow poroelastic closed spherical shell filled with fluid are studied. The frequency equation of axially symmetric vibrations for a pervious and an impervious surface is obtained. Free vibrations of a closed spherical shell are studied as a particular case when the fluid is vanished. Frequency as a function of ratio of thickness to inner radius is computed in absence of dissipation for two types of poroelastic materials each for a pervious and an impervious surface. Results of previous works are obtained as a particular case of the present study.

Keywords: Biot’s Theory, Axially Symmetric Vibrations, Radial Vibrations, Rotatory Vibrations, Spherical Shell, Elastic Fluid, Pervious Surface, Impervious Surface, Frequency

Cite this paper: nullS. Shah and M. Tajuddin, "On Axially Symmetric Vibrations of Fluid Filled Poroelastic Spherical Shells," Open Journal of Acoustics, Vol. 1 No. 2, 2011, pp. 15-26. doi: 10.4236/oja.2011.12003.

References

[1] R. Kumar, “Axially Symmetric Vibrations of a Fluid- Filled Spherical Shell,” Acustica, Vol. 21, 1969, pp. 143- 149.

[2] R. Rand and F. DiMaggio, “Vibrations of Fluid Filled Spherical and Spheroidal Shells,” Journal of the Acoustical Society of America, Vol. 42, No. 6, 1967, pp. 1278- 1286. doi:10.1121/1.1910717

[3] M. A. Biot, “Theory of Propagation of Elastic Waves in Fluid-Saturated Porous Solid,” Journal of the Acoustical Society of America, Vol. 28, 1956, pp. 168-178. doi:10.1121/1.1908239

[4] S. Paul, “A Note on the Radial Vibrations of a Sphere of Poroelastic Material,” Indian Journal of Pure and Applied Mathematics, Vol. 7, 1976, pp. 469-475.

[5] G. Chao, D. M. J. Smeulders and M. E. H. van Dongen, “Sock-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

[6] 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

[7] J. N. Sharma and N. Sharma, “Three Dimensional Free Vibration Analysis of a Homogeneous Transradially Isotropic Thermoelastic Sphere,” Journal of Applied Mechanics - Transactions of the ASME, Vol. 77, No. 2, 2010, p. 021004.

[8] S. Ahmed Shah and M. Tajuddin, “Torsional Vibrations of Poroelastic Prolate Spheroids,” International Journal of Applied Mechanics and Engineering, Vol. 16, 2011, pp. 521-529.

[9] A. Abramowitz and I. A. Stegun, “Handbook of Mathematical Functions,” National Bureau of Standards, Wa- shington, 1965.

[10] I. Fatt, “The Biot-Willis Elastic Coefficients for a Sandstone,” Journal of Applied Mechanics, Vol. 26, 1959, pp. 296-296.

[11] 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