Effect of ply orientation on the in-plane vibration of single-layer composite plates

Composite laminate structures can be designed for specific purposes by optimizing the number of plies and the ply orientations. Previous studies established the behavior of the first natural frequencies of the bending motion of a thin composite plate in the framework of classical plate theory for different boundary conditions. Since plates can also undergo in-plane vibration, the present study is aimed at investigating the effect of the ply orientation on such in-plane vibration. This is made possible through theoretical simulation with a model based on the Rayleigh–Ritz formulation in conjunction with Hamilton principle. The total matrices deduced by minimizing the Hamilton function exhibit a decoupling of bending and membrane motions, which are in plane. The natural frequencies of the membrane motion can therefore be calculated and the ply orientations are investigated for free–free boundary conditions for a square plate. The present model is first validated by comparing the natural frequencies of the bending and in-plane motions of isotropic plates with available data in the literature and the agreement is found to be excellent with the maximum discrepancy being only 0.25%. The validation is then extended to orthotropic plates for the first two bending natural frequencies under simply supported boundary conditions for different ply orientations. The present study establishes that for free–free boundary conditions the first natural frequency of the in-plane vibration of a composite square plate is symmetrical with respect to 45∘45∘ ply orientation and is maximum for this value. This study suggests that it is possible to use this analysis to design composite plates by properly tailoring ply orientations.