Dispersion of elastic waves in a strongly inhomogeneous three-layered plate

Prikazchikov, Danila; Kaplunov, Julius; Prikazchikova, Liudmila

Abstract

Elastic wave propagation in a three-layered plate with high-contrast mechanical and geometric properties of the layers is analysed. Four specific types of contrast arising in engineering practice, including the design of stiff and lightweight structures, laminated glass, photovoltaic panels, and electrostatic precipitators in gas filters, are considered. For all of them the cut-off frequency of the first harmonic is close to zero. Two-mode asymptotic polynomial expansions of the Rayleigh-Lamb dispersion relation approximating both the fundamental bending wave and the first harmonic, are derived. It is established that these can be either uniform or composite ones, valid only over non-overlapping vicinities of zero and the lowest cut-off frequencies. The partial differential equations of motion associated with two-mode shortened dispersion relations are also presented.

Citation

Prikazchikov, D., Kaplunov, J., & Prikazchikova, L. (2017). Dispersion of elastic waves in a strongly inhomogeneous three-layered plate. International Journal of Solids and Structures, 113-114, 169-179. https://doi.org/10.1016/j.ijsolstr.2017.01.042

• Journal Article Type: Article
• Acceptance Date: Jan 29, 2017
• Online Publication Date: Feb 3, 2017
• Publication Date: May 15, 2017
• Journal: International Journal of Solids and Structures
• Print ISSN: 0020-7683
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 113-114
• Pages: 169-179
• DOI: https://doi.org/10.1016/j.ijsolstr.2017.01.042
• Keywords: waves, mathematics, physics
• Public URL: https://keele-repository.worktribe.com/output/407832
• Publisher URL: http://dx.doi.org/10.1016/j.ijsolstr.2017.01.042