Non-linear modulation of SH waves in a two-layered plate and formation of surface SH waves

Non-linear modulation of 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. The problem is investigated by a perturbation method and in the analysis it is assumed that between the linear shear velocities of the top layer, c₁, and the bottom layer, c₂, the inequality c₁<c₂ is valid. In the layered structure then an SH wave exists if the wave velocity c of the wave satisfies either the condition c₁<c≤c₂ or the one c₁<c₂≤c. Here the problem is examined under the former condition and it is shown that the non-linear modulation of SH waves is governed by a non-linear Schrödinger equation. In this case the formation of surface SH (Love) waves is also revealed if the top layer is thinner when compared with the bottom layer. Then the stability condition is discussed and the existence of bright (envelope) and dark solitons are manifested.