A COMPARISON OF SOME SHELL THEORIES USED FOR THE DYNAMIC ANALYSIS OF CROSS-PLY LAMINATED CIRCULAR CYLINDRICAL PANELS

The free vibration problem of thin elastic cross-ply laminated circular cylindrical panels is considered. For this problem, a theoretical unification as well as a numerical comparison of the thin shell theories most commonly used (in engineering applications) is presented. In more detail, the problem is formulated in such a way that by using some tracers, which have the form of Kronecker's deltas, the stress-strain relations, constitutive equations and equations of motion obtained produce, as special cases, the corresponding relations and equations of Donnell's, Love's, Sanders' and Flugge's theories. By using a closed form solution, obtained for simply supported panels, a comparison of corresponding numerical results obtained on the basis of all of the aforementioned shell theories is attempted.