The effects of kinematic model approximations on natural frequencies and modal damping of laminated composite plates

The present work deals with the effects of kinematics on the natural frequencies and modal damping of laminated composite plates. Three theories are considered, the classical laminated plate theory (CLPT), the first-order shear deformation theory (FSDT) and the third-order shear deformation theory (TSDT). The displacement field corresponding to a simply supported square laminated composite plate is introduced in the energy equation. The governing equations are then formulated for the laminated composite plates using the Hamiltonian principle. Equations of motion are established and then the harmonic free vibrations are studied. The complex frequencies are obtained from the characteristic equation, which gives the natural frequencies and the modal damping for each ( m , n ) mode. The effects of stacking sequence, rotary inertia and thickness to side ratio ( h / a ) on the natural frequencies and modal damping ratios are analyzed. The results lead to conclusions about the applicability of each of the plate theories CLPT, FSDT and HSDT.