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 sti outer layers. In all types of contrast, the
value of the cut-o 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 justied boundary conditions are derived by the generalisation of the
Saint Venant's principle to high-contrast structures.