Three-Dimensional Free Vibration Analysis of Cross-Ply Laminated Rectangular Plates with Free Edges Through a Displacement-Based Approach

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.