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

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.