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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.

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.

For the numerical purpose, the solids Berea sandstone and bone are used. The results are presented graphically.

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.

The purpose of this paper is to investigate the effect of initial stress and heterogeneity on the propagation of torsional waves in dissipative medium. The problem consists of dry sand poroelastic half-space embedded between heterogeneous self-reinforced half-space and poroelastic medium. The frequency equation is derived in the framework of Biot's theory with some variants.

Torsional wave propagation in dry sand poroelastic half-space embedded between self-reinforced half-space and poroelastic medium. All the constituents here are assumed to be dissipative, heterogeneous and initial stressed.

Phase velocity and attenuation are computed against wavenumber for various values of self-reinforcement parameter, inhomogeneity parameter and initial stress. Particular cases are discussed in absence of dissipation. The numerical results are presented graphically.

Initial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium are investigated. The frequency equation is derived, and which intern gives the phase velocity and attenuation coefficient for various values of initial stress, self-reinforcement parameter and heterogeneity parameter. From the numerical results, it is clear that as wavenumber varies phase velocity and attenuation are periodic in nature for all the cases. Particular cases are discussed in absence of dissipation. This kind of analysis can be extended to any elastic solid by taking magnetic, thermo and piezoelectric effects into account.

The purpose of this paper is to investigate the effect of reinforcement, inhomogeneity and initial stress on the propagation of shear waves. The problem consists of magneto poroelastic medium sandwiched between self-reinforced medium and poroelastic half space. Using Biot’s theory of wave propagation, the frequency equation is obtained.

Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium and poroelastic half space is investigated. This particular setup is quite possible in the Earth crust. All the three media are assumed to be inhomogeneous under initial stress. The significant effects of initial stress and inhomogeneity parameters of individual media have been studied.

Phase velocity is computed against wavenumber for various values of self-reinforcement, heterogeneity parameter and initial stress. Classical elasticity results are deduced as a particular case of the present study. Also in the absence of inhomogeneity and initial stress, frequency equation is discussed. Graphical representation is made to exhibit the results.

Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium, and poroelastic half space are investigated in presence of initial stress, and inhomogeneity parameter. For heterogeneous poroelastic half space, the Whittaker’s solution is obtained. From the numerical results, it is observed that heterogeneity parameter, inhomogeneity parameter and reinforcement parameter have significant influences on the wave characteristics. In addition, frequency equation is discussed in absence of inhomogeneity and initial stress. For the validation purpose, numerical results are also computed for a particular case.