Geometrically nonlinear free vibration analysis of laminated composite plates: A finite element assessment of a higher order non-polynomial shear deformation theory

In the current work, a higher order non-polynomial theory based upon nonlinear distribution of transverse shear stresses along the plate thickness is employed to apprehend the geometrically nonlinear free vibration of laminated composite plates. The present theory satisfies the zero traction at the top and bottom of the laminated plate. By considering the Lagrange equation, the governing equations of motion are derived and discretized using finite element procedure. The displacement field function is reflected with seven degrees of freedom. For the analysis, various types of laminates including symmetric, anti-symmetric, cross and angle-ply with various edge supports are considered.