Three-dimensional free vibration analysis of levy-type laminated plates using multi-term extended Kantorovich method

A closed form three-dimensional (3D) free vibration solution for a rectangular laminated plate with Levy-type support conditions is presented first time using recently developed extended Kantorovich method. Hamiltons principle is extended to develop a mixed formulation in terms of displacements and stresses as primary variables. The present solution will serve as a benchmark for assessing two-dimensional (2D) theories and 3D numerical solutions. Natural frequencies are tabulated for composite and sandwich laminates (first time) for different boundary conditions. It is found that single term solution is sufficient enough for obtaining accurate natural frequencies. But stresses near the clamped edge are accurately predicted by multi-term solution (n = 2). The effect of the span to thickness ratio and in-plane modulus ratios on the natural frequency is also studied.