COUPLED WAVES IN A BAR OF MOONEY-RIVLIN MATERIAL

Equations governing the motion of a Mooney-Rivlin material cylindrical bar with torsion-extension coupled modes are solved by the use of similarity methods and an explicit MacCormack type of finite difference scheme. Effects of parametric ratio of the Mooney-Rivlin materials, time histories and wave profiles for semi-infinite and finite bars are discussed. The solution space plot distinguishing the simple waves, loading shocks and unloading shocks is provided for extreme values of the material parameter. Specific cases of semi-infinite and free-fixed finite bars with torque and axial force loadings corresponding to simple waves and loading shocks are presented. The results show that the nature of wave profiles for semi-infinite bars remains same for the Mooney-Rivlin material as compared with its derivative the neo-Hookean material. However, for finite bars the difference is significant due to wave reflections from boundaries.