Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates

Lenser A. Aghalovyan, Lusine G. Ghulghazaryan, Julius Kaplunov () and Danila Prikazchikov
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Lenser A. Aghalovyan: Institute of Mechanics, National Academy of Sciences of the Republic of Armenia, Yerevan 0019, Armenia
Lusine G. Ghulghazaryan: Institute of Mechanics, National Academy of Sciences of the Republic of Armenia, Yerevan 0019, Armenia
Julius Kaplunov: School of Computer Science and Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UK
Danila Prikazchikov: School of Computer Science and Mathematics, Keele University, Keele, Staffordshire ST5 5BG, UK

Mathematics, 2023, vol. 11, issue 18, 1-11

Abstract: The effect of high contrast on the multiscale behaviour of elastic laminates is studied. Mathematical modelling in this area is of significant interest for a variety of modern applications, including but not limited to advanced sandwich structures and photovoltaic panels. As an example, the antiplane shear of a symmetric, three-layered plate is considered. The problem parameters expressing relative thickness, stiffness and density are assumed to be independent. The high contrast may generally support extra length and time scales corresponding to degenerated boundary layers and propagating long-wave low-frequency vibration modes. The main focus is on the relation between these two phenomena. The developed multiparametric approach demonstrates that those do not always appear simultaneously. The associated explicit estimates on contrast parameters are established. In addition, the recent asymptotic extension of the classical Saint-Venant’s principle is adapted for calculating the contribution of the degenerate boundary layer or long-wave low-frequency propagation mode. The peculiarity of the limiting absorption principle in application to layered media is also addressed.

Keywords: laminate; high contrast; multiparametric; multiscale; asymptotic; Saint-Venant’s principle; boundary layer; long-wave; low-frequency; radiation conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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