Asymptotic formulations of anti-plane problems in pre-stressed compressible elastic laminates

• DOI: 10.1515/phys-2022-0265
• Publication Date: 2023-07-29T17:11:14Z
• Authors: Maha M. Helmi; Saad Althobaiti; Ali M. Mubaraki; Graham A. Rogerson
• Keywords: Asymptotic expansion; Dispersion relation

Abstract This article investigates the long-wave anti-plane shear motion in a symmetric three-layered laminate composed of pre-stressed compressible elastic layers. The layers are perfectly bonded, while traction-free and fixed boundary conditions considered on outer faces laminate. In both cases, dispersion relation is obtained terms anti-symmetric decompositions. Numerical results an asymptotic analysis presented, corresponding to three possible vibration modes. It revealed that low-frequency mode only exists respect with free-faces, all other cases pose series non-zero cut-off frequencies. Comparisons between exact approximate excellent agreement observed.