Free vibration and buckling of symmetric cross-ply lanimated rectangular plates and isotropic open circular cylindrical shells are studied in this thesis.

To reduce the number of boundary conditions that must be studied toward the completion of free vibration analysis of rectangular plates and open circular cylindrical shells, the author proposed the concept of basic plates and basic shells. O nly solutions for basic plates and basic shells need be investigated in order to obtain solutions for all the plates and shells using the method of superposition. There are only six basic plates and thirteen basic shells while the total rectangular plates and open circular cylindrical shells distinguished by different arrangements of boundary conditions axe 21 and 18,496, respectively.

Accurate analytical solutions for till basic plates and shells may be obtained using the generalized Navier method, generalized Levy method and the method of superposition fully developed in the thesis for the analysis of rectangular laminates and cylindrical shells. Numerical computations based on the method of superposition have shown that only a few terms are needed to achieve the desired accuracy for eigenvalues of plates and shells.

In treating free flexural vibration problem of rectangular plates having a linear crack, the author proposed an analytical technique. It is found to be extremely satisfactory for eigenvalue calculations of higher vibration inodes.