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Three-dimensional free vibration analysis of cross-ply laminated rectangular plates with free edges through a displacement-based approach
Arcangelo Messina*
and
Giosuè Rollo
Università del Salento
* To whom correspondence should be addressed. E-mail: arcangelo.messina{at}unisalento.it.
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Abstract |
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This paper presents a model belonging to a theory that recently appeared in the literature dealing with accurate solutions of freely vibrating laminated plates. The present model, which is derived from a displacement-based variational approach, investigates both free edge boundary conditions and the possibility of obtaining accurate results without explicitly incorporating stress interlaminar continuity conditions where they are in principle requested. These investigations are carried out within the frame of multi-layered plates where the literature is lacking in relevant three-dimensional results.
In spite of the multi-layer nature of the plate, the model is developed as if the same plate were virtually made of a single layer because a suitable set of piecewise-smooth functions is used. Once the model is theoretically introduced, natural frequencies are evaluated for the case of plates with simply supported and free edge boundaries. The evaluations are compared with those few existing values of exact or approximate three-dimensional models, new results are provided for future comparisons and, finally, the performance of the model is tested with respect to extreme cases which could also deal with interesting engineering applications without reverting to non-immediate numerical schemes.
First published on June 5, 2009
Mathematics and Mechanics of Solids 2009, doi:10.1177/1081286509104778
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