Asymptotic analysis of an anti-plane shear dispersion of an elastic five-layered structure amidst contrasting properties

Abstract

The present paper studies the anti-plane shear motion of an inhomogeneous elastic five-layered plate amidst the four contrasting material setups. The asymptotic analysis method in regard to the various material parameters is adopted for the study. The respective displacements, stresses and the Rayleigh-Lamb dispersion relation corresponding to the antisymmetric anti-plane motion with perfect interlayer and traction-free (on the outer faces) boundary conditions are determined. Furthermore, in order to analyze the said dispersion relation in the presence of these contrasts, a unification of parameters was proposed. The overall cutoff frequencies and the low-frequency estimates are determined for both the generalized and unified settings. A comparative analysis between the unified Rayleigh-Lamb dispersion relation and the optimal shortened polynomial dispersion relation is carried for each contrast. We also established some asymptotic formulae for the related unified displacements and stresses.