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

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.