An approximation technique is considered for computing transmission and reflection coefficients for propagation of an elastic pulse through a planar slab of finite width. The propagation of elastic pulse through a planar slab is derived from first principles using straightforward time-dependent method. The paper ends with calculations of enhancement factor for the elastic plane wave and it is shown that it depends on the velocity ratio of the wave in two different media but not the incident wave form. The result, valid for quite arbitrary incident pulses and quite arbitrary slab inhomogeneities, agrees with that obtained by time-independent methods, but uses more elementary methods. Manuscript profile

This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the non-homogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The non-homogeneous viscoelastic rods are assumed to be initially unstressed and at rest. In this study, it is assumed that density, rigidity and viscosity of the specimen i.e. rod are space dependent. The method of non-linear partial differential equation (Eikonal equation) has been used for finding the dispersion equation of harmonic waves in the rods. A method for treating reflection at the free end of the finite non-homogeneous viscoelastic rod is also presented. All the cases taken in this study are discussed numerically and graphically with MATLAB. Manuscript profile

The effect of magnetic field on torsional waves propagating in non-homogeneous viscoelastic cylindrically aeolotropic material is discussed. The elastic constants and non-homogeneity in viscoelastic medium in terms of density and elastic constant is taken. The frequency equations have been derived in the form of a determinant involving Bessel functions. Dispersion equation in each case has been derived and the graphs have been plotted showing the effect of variation of elastic constants and the presence of magnetic field. The obtained dispersion equations are in agreement with the classical result. The numerical calculations have been presented graphically by using MATLAB. Manuscript profile

The propagation of torsional waves in a prestressed fiber-reinforced half-space under the effect of magnetic field and gravity has been discussed. The problem has been solved analytically using Whittaker function to obtain the exact solution frequency equations. Numerical results for stress, gravity and magnetic field are given and illustrated graphically. Comparisons are made with the results predicted by the boundary value condition for rigid boundary and for traction free boundary in the presence and in the absence of the effect of a magnetic field, gravity and stress. It is found that the reinforcement, gravity and magnetic field have great effects on the distribution. Manuscript profile

The purpose of this paper is to analysis the viscoelastic models under dynamic loading.A five-parameter model is chosen for study exhibits elastic, viscous, and retarded elastic response to shearing stress. The viscoelastic specimen is chosen which closely approximates the actual behavior of a polymer. The module of elasticity and viscosity coefficients are assumed to be space dependent i.e. functions of in non-homogeneous case and stress-strain are harmonic functions of time The expression for relaxation time for five parameter viscoelastic model is obtained by using constitutive equation. The dispersion equation is obtained by using Ray techniques. The model is justified with the help of cyclic loading for maxima or minima. Manuscript profile