Trigonometric zigzag theory for free vibration and transient responses of cross-ply laminated composite plates

In this article, an application of the non-polynomial zigzag theory is presented to analytically derive the free vibration and transient responses of multilayered laminated composites and sandwich plates. The non-linear variations of the transverse shear stresses are incorporated in the mathematical model with the help of a trigonometric function, namely the secant function. The inter-laminar continuity conditions are artificially enforced at the layer interfaces that reduce the total number of field variables to five like the first-order shear deformation theory (FSDT). The present kinematic field yields more accurate results than the FSDT and also removes the requirement of any shear correction factor. The governing equilibrium equations of motion are obtained using Hamilton's principle and solved with Navier's solution technique. The responses from the coupled ordinary differential equations in time are obtained with the Newmark's time integration scheme. Numerical problems on the diaphragm supported laminated composites, and soft-core-sandwich plates are solved analytically to derive the free vibration and transient responses by taking into consideration the several geometrical and material features of the plate structures. The responses are also compared with the benchmark elasticity solutions and solutions reported in the literature from other shear deformation models. An exhaustive study on the transient analysis is presented by solving several problems of laminated composite plates that are subjected to various time-dependent loads and various forms of blast loads.