Interaction of nonlinear sh waves in a two layered elastic plate

In this work, nonlinear interaction of two co-directional shear horizontal (SH) waves in a two-layered elastic plate of uniform thickness is considered. Both layers are assumed to be homogeneous, isotropic and incompressible elastic and having different mechanical properties. Stress and displacements are continuous at the interface of the layers. Also, free surfaces of the layers are free of tractions. Under these assumptions, the equations of motion and boundary conditions governing the propagation of nonlinear SH waves in this elastic media are derived. The boundary value problem describing the wave motion is examined asymptotically by employing a perturbation method. It is shown that the first order slowly varying amplitudes of interacting waves are governed asymptotically by two coupled nonlinear Schrödinger (CNLS) equations. The linear instabilities of solutions for CNLS equations and the existence of solitary wave solutions are examined when the group velocities of interacting waves are equal. In addition, the effect of material nonlinearity on the interaction of two co-directional SH waves propagating in the elastic plate is studied.