Asymptotic analysis of multi-layered waveguides with contrast parameters

Abstract

The research is investigating anti-plane shear of a strongly inhomogeneous dynamic asymmetric laminate. Two types of contrast are considered, including those for composite structures with thick or thin stiff outer layers. In all types of contrast, the value of the cut-off frequency corresponding to the lowest harmonic tends to zero. For two modes, i.e. the fundamental mode and aforementioned lowest harmonic, the shortened dispersion relations and the associated formulae for displacement and stresses are obtained. As a particular case a symmetric three-layered plate is studied. The asymptotic equations of motion are derived with the evaluation of the validity range for each of two considered setups of contrast parameters. In addition, the asymptotically justified boundary conditions are derived by the generalisation of the Saint Venant's principle to high contrast structures.