The plane-strain traveling waves in a pre-stressed Single viscoelastic plate

Within the framework of the uniformly homogeneous anisotropic model with utilization of the two-dimensional linearized theory of elastic waves in pre-stressed body, the mathematical modeling of the plane wave propagation containing viscoelastic plate of finite thickness and infinite extent has been proposed. The objective of this study is to find the influence of plane wave at the edge of a pre-stressed viscoelastic plate.The dispersion and damping equations are established from the frequency equation of plane wave. The effects of viscosity parameter, compressive and tensile initial stresses on the phase velocity and damped velocity of plane wave are studied and elucidated by means of graphs. As the special case of the problem it is shown that plane wave do not propagate when the isotropic plate is very thin (case-1) and also when wavelength is very small compared with the isotropic plate thickness (case-2) under no initial stress. The expression for group velocity has been obtained in closed form in both the cases when the plate is anisotropic (case 3) and isotropic (case 4) without initial stress. This is one of the major highlight of this problem. Moreover, some important peculiarities have been traced out by means of graphs.