Vol. 7, No. 1, 2019

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Analytical solutions for the natural frequencies of rectangular symmetric angle-ply laminated plates

Florence Browning and Harm Askes

Vol. 7 (2019), No. 1, 51–61
DOI: 10.2140/memocs.2019.7.51

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.

laminated plate, natural frequencies, anisotropy, elasticity
Physics and Astronomy Classification Scheme 2010
Primary: 43.40.+s, 46.40.-f
Mathematical Subject Classification 2010
Primary: 74G10, 74H45
Received: 17 July 2018
Revised: 29 August 2018
Accepted: 24 October 2018
Published: 22 April 2019

Communicated by Francesco dell'Isola
Florence Browning
Interrobang Architecture and Engineering
Webb Yates Engineers Ltd
United Kingdom
Harm Askes
Department of Civil and Structural Engineering
University of Sheffield
United Kingdom