Free vibration analysis of laminated composites plates and cylindrical shallow shells

In this work, free vibration characteristics of cross-ply laminated composite plates and cylindrical shallow shells have been studied with varying anisotropy and curvature properties. Shallow shells have been assumed to have varying thickness, curvature and elasticity modulus ratios. In the analysis, first, kinematic relations of strains and deformations have been obtained. Then, using Hamilton?s principle, the governing differential equations have been obtained for a general curved shell. In the next step, stress-strain relation for laminated, cross-ply composite shells has been given. By means of some assumptions and simplifications employing Fourier series as a displacement field, differential equations for shallows shells have been written and solved in matrix form. Employing the computer algebra system called MATHEMATICA, a computer program has been prepared for the solution. The results obtained by this solution have been given in the form of tables and graphs. The example problems have been solved also by (ANSYS and SAP2000) programs, which are based on the finite element method (FEM), and compared with the previous ones.