Kaplunov, J, Erbaş, B and Ege, N (2022) Asymptotic derivation of 2D dynamic equations of motion for transversely inhomogeneous elastic plates. International Journal of Engineering Science, 178 (103723). ISSN 0020-7225

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The 3D dynamic equations in elasticity for a thin transversely inhomogeneous plate are subject to asymptotic analysis over the low-frequency range. The leading and first order approximations are derived. The former is given by a biharmonic equation on the mid-plane generalizing the classical Kirchhoff equation for plate bending. A simple explicit formula for the effective bending stiffness is presented. The refined first order equation involves the same biharmonic operator, as the leading order one, along with corrections expressed through Laplacians. However, the constant coefficients at these corrections take the form of sophisticated repeated integrals across the plate thickness. The formulae for the transverse variations of the displacement and stress components, especially relevant for FGM structures, are also obtained. The scope for comparison of the developed asymptotic results and the existing ad hoc considerations on the subject seems to be limited, in contrast to the homogeneous setup, due to a more substantial deviation between the predictions offered by these two approaches.

Item Type: Article
Additional Information: The final version of this article and all relevant information related to it, including copyrights, can be found on the publisher website.
Subjects: G Geography. Anthropology. Recreation > G Geography (General)
Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Related URLs:
Depositing User: Symplectic
Date Deposited: 07 Sep 2022 09:08
Last Modified: 07 Sep 2022 09:08
URI: https://eprints.keele.ac.uk/id/eprint/11400

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