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

Helmi, Maha M.; Althobaiti, Saad; Mubaraki, Ali M.; Rogerson, Graham A.

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

Citation

Helmi, M. M., Althobaiti, S., Mubaraki, A. M., & Rogerson, G. A. (2023). Asymptotic formulations of anti-plane problems in pre-stressed compressible elastic laminates. Open Physics, 21(1), https://doi.org/10.1515/phys-2022-0265

• Journal Article Type: Article
• Acceptance Date: Jun 5, 2023
• Online Publication Date: Jul 29, 2023
• Publication Date: Jul 29, 2023
• Deposit Date: Jan 23, 2024
• Journal: Open Physics
• Print ISSN: 2391-5471
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 1
• DOI: https://doi.org/10.1515/phys-2022-0265
• Keywords: General Physics and Astronomy
• Publisher URL: https://www.degruyter.com/document/doi/10.1515/phys-2022-0265/html