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Asymptotic approach to anti‐plane dynamic problem of asymmetric three‐layered composite plate
Author(s) -
Ibrahim Nuruddeen Rahmatullah,
Nawaz R.,
Zaigham Zia Q. M.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7456
Subject(s) - mathematics , dispersion relation , mathematical analysis , plane (geometry) , shear (geology) , plate theory , dispersion (optics) , range (aeronautics) , equations of motion , classical mechanics , geometry , physics , materials science , optics , composite material , boundary value problem
In this manuscript, the anti‐plane shear motion of an asymmetric three‐layered inhomogeneous elastic plate is examined. An asymptotic approach is employed for the present investigation. Both thgeneralized and unified dispersion relations within the long‐wave low‐frequency range have been successfully determined. The obtained unified dispersion relation is investigated taking into account the recently analyzed material contrast for layered plates with mixed stiff‐soft layers of different material properties. The asymptotic formulae for the respective fields in addition to the determination of approximate equations of motions have also been presented. A comparative study with the symmetric plate is made; being a special case of the asymmetric plate under consideration. In the end, we provide some deductions and concluding remarks.