Browning, F. and Askes, H. orcid.org/0000-0002-4900-1376 (2019) Analytical solutions for the natural frequencies of rectangular symmetric angle-ply laminated plates. Mathematics and Mechanics of Complex Systems, 7 (1). pp. 51-61. ISSN 2326-7186
Abstract
Analytical solutions, based on the Ritz method, are derived for the lowest natural frequency of rectangular symmetric angle-ply laminated plates. Since symmetric angle-ply plates have nonzero cross-elasticity constants, the solutions are approximate. The accuracy of these solutions is tested with a convergence study using the Rayleigh quotient iteration method. With the solutions available in symbolic form, parameter studies are presented that establish the effect of plate aspect ratio and ply orientation angle for a number of stacking geometries. The results are also verified through a comparison with numerical Ritz solutions, showing a maximum error of 5% in our approximate solution.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Mathematical Sciences Publishers. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | laminated plate; natural frequencies; anisotropy; elasticity |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Jan 2019 12:55 |
Last Modified: | 29 Aug 2019 09:29 |
Status: | Published |
Publisher: | Mathematical Sciences Publishers |
Refereed: | Yes |
Identification Number: | 10.2140/memocs.2019.7.51 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:138316 |