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 firstorder shear deformation plate theory (fsdt). general layups are evaluated by the assumption of crossply and angleply 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 bendingstretching coupling lowers the vibration frequencies for both crossply and angleply laminates with the clpt. also it is found that the effect of bendingstretching coupling, transverse shear deformation and rotary inertia is to lower the fundamental frequencies.