An asymptotic investigation of the dynamics and dispersion of an elastic five-layered plate for anti-plane shear vibration

Abstract

An asymptotic approach of analysis is used to analyze the antisymmetric anti-plane shear dispersion of an elastic inhomogeneous five-layered plate in the presence of material contrasts. The resultant exact dispersion relation, overall cut-off frequency and the low-frequency range are determined. Two different asymptotic contrasting material setups for layered plates are employed with regards to the optimal shortened polynomial dispersion relation in the context of the structure under consideration. The asymptotic behaviors of the displacements and stresses in the respective layers of the plate are also examined. Finally, we provided some concluding remarks.