Two dimensional wave propagation in a rotating elastic material with voids
Prof. Sushil Tomar (Panjab University)
Friday 20th March, 2009 14:00-15:00 204
Two-dimensional wave propagation is studied in a uniform elastic material with voids rotating with constant angular velocity. A theory of elastic material with voids developed by Iesan (1986)[A theory of thermo-elastic material with voids, Acta Mechanica, 60, 67-89] has been used for the mathematical treatment. It is found that there exist three coupled plane waves propagating with distinct phase speeds. The void parameters and the rotation of the medium are responsible for this coupling. In the absence of void parameters, the classical longitudinal and transverse waves are found to be coupled through the rotation parameter. At very large frequency, it is found that these waves are decoupled and propagate with distinct phase speeds. These are (i) a longitudinal wave (ii) a transverse wave and (iii) a longitudinal wave corresponding to the change in void volume fraction. The former two are the same waves as in classical elasticity, while the latter is new and appears due to the presence of the voids in the medium. No effect of rotation of the body is observed in this particular situation. The reflection phenomena of these waves have also been investigated at the free plane boundary of a rotating elastic half-space with voids. Formulae for reflection coefficients of various reflected waves are derived. It is found that these coefficients are functions of the elastic properties of the medium and the angle of incidence. To study the problem in greater details, we have planned to study the various aspect of the problem numerically. For this purpose, the numerical computations for a specific model are in progress.