On the free vibration of angle-ply laminated composite and soft core sandwich plates

In the present study, a simple four-variable trigonometric shear deformation theory considering the effects of transverse shear deformation and rotary inertia is evaluated for the free vibration analysis of antisymmetric laminated composite and soft core sandwich plates. The theory is displacement-based equivalent single-layer theory in which the in-plane displacements use trigonometric function in terms of thickness coordinate, for calculating out-of-plane shearing strains. The number of unknown variables involved in the present theory is only four as against five or more than five in case of other higher order theories. The equations of motion are obtained using the principle of virtual work. A closed-form solution for equations of motion is obtained using the Navier's solution technique. The effects of side-to-thickness ratio, modular ratio and fibre angle are critically assessed for several problems of laminated composite and sandwich plates. The natural frequencies obtained by using present theory are verified by comparing the results with those of other theories and exact elasticity solution wherever applicable.