A Numerical and Analytical Solution for the Free Vibration of Laminated Composites Using Different Plate Theories

An analytical and numerical solution for the free vibration of laminated polymeric composite plates with different layups is studied in this paper. The governing equations of the laminated composite plates are derived from the classical laminated plate theory (CLPT) and the first-order shear deformation plate theory (FSDT). General layups are evaluated by the assumption of cross-ply and angle-ply laminated plates. The solver is coded in MATLAB. As a verification method, a finite element code using ANSYS is also developed. The effects of lamination angle, plate aspect ratio and modulus ratio on the fundamental natural frequencies of a laminated composite are also investigated and good agreement is found between the results evaluated and those available in the open literature. The results show that the fundamental frequency increases with the modular ratio and the bending-stretching coupling lowers the vibration frequencies for both cross-ply and angle-ply laminates with the CLPT. Also it is found that the effect of bending-stretching coupling, transverse shear deformation and rotary inertia is to lower the fundamental frequencies.