Analysis of radial vibrations in thick walled hollow poroelastic cylinder in the framework of Biot’s extension theory
Multidiscipline Modeling in Materials and Structures
ISSN: 1573-6105
Article publication date: 15 June 2018
Issue publication date: 29 October 2018
Abstract
Purpose
In this paper, wave propagation in a poroelastic thick-walled hollow cylinder is investigated in the framework of Biot’s extension theory. Biot’s theory of poroelasticity is valid for isotropic porous solids saturated with non-viscous fluid. The bulk and shear viscosities are not considered in the classical Biot’s theory. Biot’s extension theory takes all these into an account. Biot’s extension theory is applied here to investigate the radial vibrations in thick-walled hollow poroelastic cylinder. The paper aims to discuss these issues.
Design/methodology/approach
By considering the stress-free boundaries, the frequency equation is obtained in the presence of dissipation. Limiting case when the ratio between thickness and inner radius is very small is investigated numerically. In the limiting case, the asymptotic expansions of Bessel functions are employed so that frequency equation is separated into two parts which gives attenuation coefficient and phase velocity. If the shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory.
Findings
For the numerical purpose, the solids Berea sandstone and bone are used. The results are presented graphically.
Originality/value
Radial vibrations of thick-walled hollow poroelastic cylinder are investigated in the framework of Biot’s extension theory. Due to the mathematical complexity, limiting case is considered. The complex valued frequency equation is discussed numerically which gives the attenuation coefficient and phase velocity. If shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory. The comparison has been made between the current results and that of classical results.
Keywords
Acknowledgements
Rajitha Gurijala acknowledges University Grants Commission (UGC), Government of India for its financial support through the Postdoctoral Fellowship for Women (Grant Number F.15-1/2015-17/PDFWM-2015-17-TEL-34525 (SA-II)).
Citation
Gurijala, R. and Perati, M.R. (2018), "Analysis of radial vibrations in thick walled hollow poroelastic cylinder in the framework of Biot’s extension theory", Multidiscipline Modeling in Materials and Structures, Vol. 14 No. 5, pp. 970-983. https://doi.org/10.1108/MMMS-11-2017-0136
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited