Elastodynamic analysis of anisotropic liquid-saturated porous medium due to mechanical sources

Elastodynamic analysis of an anisotropic liquid-saturated porous medium is made to study a deformation problem of a transversely isotropic liquid-saturated porous medium due to mechanical sources. Certain physical problems are of the nature, in which the deformation takes place only in one direction, e.g., the problem relating to deformed structures and columns. In soil mechanics, an assumption of only vertical subsidence is often invoked and this leads to the one dimensional model of poroelasticity. By consid- ering a model of one-dimensional deformation of the anisotropic liquid-saturated porous medium, variations in disturbances are observed with reference to time and distance. The distributions of displacements and stresses are affected due to the anisotropy of the medium, and also due to the type of sources causing the disturbances.

Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces

In this paper, we suggest a new type of three step iterative scheme called the CR iterative scheme and study the strong convergence of this iterative scheme for a certain class of quasi-contractive operators in Banach spaces. We show that for the aforementioned class of operators, the CR iterative scheme is equivalent to and faster than Picard, Mann, Ishikawa, Agarwal et al., Noor and SP iterative schemes. Moreover, we also present various numerical examples using computer programming in C++ for the CR iterative scheme to compare it with the other above mentioned iterative schemes. Our results show that as far as the rate of convergence is concerned 1) for increasing functions the CR iterative scheme is best, while for decreasing functions the SP iterative scheme is best;2) CR iterative scheme is best for a certain class of quasi-contractive operators.

On Propagation of Rayleigh Type Surface Wave in a Micropolar Piezoelectric Medium

In the present paper, the governing equations of a linear transversely isotropic micropolar piezoelectric medium are specialized for x-z plane after using symmetry relations in constitutive coefficients. These equations are solved for the general surface wave solutions in the medium. Following radiation conditions in the half-space, the particular solutions are obtained, which satisfy the appropriate boundary conditions at the stress-free surface of the half-space. A secular equation for Rayleigh type surface wave is obtained. An iteration method is applied to compute the non-dimensional wave speed of the Rayleigh surface wave for specific material parameters. The effects of piezoelectricity, non-dimensional frequency and non-dimensional material constant, charge free surface and electrically shorted surface are shown graphically on the wave speed of Rayleigh wave.

Radiative Effect on Flow and Heat Transfer over a Vertically Oscillating Porous Flat Plate Embedded in Porous Medium with Oscillating Surface Temperature

The effect of radiation on flow and heat transfer over a vertically oscillating porous flat plate embedded in porous medium with oscillating surface temperature is investigated. The analytic solutions of momentum and energy equations are obtained. The velocity and temperature profiles are computed. The frictional force at the plate due to viscosity of fluid is estimated in terms of non dimensional skin friction coefficient and heat convection at the plate is estimated in the form of Nusselt number. The effects of physical parameters Prandtl number Pr, Grashof number Gr, Suction parameter S and radiative parameter R on velocity and temperature profiles are analyzed through graphs. The effects of oscillation on the velocity and temperature profiles are shown through 3-D surface plot.

Reflection and transmission of elastic waves at an interface between two micropolar piezoelectric half-spaces

In the present paper,we consider a problem of reflection and transmission of plane waves at an interface between two different transversely isotropic micropolar piezoelectric half-spaces.The plane wave solution of governing equations for micropolar piezoelectric medium indicates the propagation of three coupled plane waves.An incident plane wave at an interface between two dissimilar half-spaces generates three reflected and three transmitted waves.The relations between amplitude ratios of reflected and transmitted waves are derived which,in general,depend on material parameters and angle of incidence.The explicit expressions for energy ratios of reflected and transmitted waves are also obtained.For relevant material parameters,the results are illustrated graphically to show the micropolar piezoelectric effects on variations of amplitude ratios and the square root of energy ratios against the angle of incidence.