Assessment of zigzag theories for free vibration analysis of laminated-composite and sandwich plates

In this work, inverse hyperbolic zigzag theory and inverse trigonometric zigzag theory, recently developed by the authors, are extended for the free vibration analysis of the laminated composite and sandwich plates. The developed plate models satisfy the condition of transverse shear stress continuity at the layer interfaces and the zero traction boundary conditions on the surfaces of the plate obviating the need of shear correction factor. They consider shear strain shape function assuming the nonlinear distribution of transverse shear stresses. The less numbers of independent variables makes the solution computationally effective. An efficient C⁰ continuous isoparametric serendipity element is employed for the usual discretization of the plate structure. In order to demonstrate the capabilities of the developed models in predicting the structural free vibration response, some representative results are obtained covering different features of laminated composite and sandwich structures such as boundary conditions, aspect ratios and span-to-thickness ratios and the results are compared with those in the literature wherever available. The excellent agreement of the evaluated results with the three-dimensional exact results conclude that the presented models are not only accurate but also efficient.