Free vibration of two-layered cross-ply laminated plates using layer-wise trigonometric shear deformation theory

In this paper, variationally consistent layer-wise trigonometric shear deformation theory has been extended to deal with free vibration of two-layered laminated cross-ply plates. Governing differential equations are derived by making use of a displacement field which allows a sinusoidal variation of the in-plane displacements through the laminate thickness. In this displacement based theory, constitutive relations between shear-stress and shear-strains are satisfied in both the layers, and, therefore, shear correction factor is not required. Compatibility at the layer interface in respect of in-plane displacement and compatibility in respect of transverse shear-stress is satisfied, yet present theory contains fewer unknown variables than that of the first order shear deformation theory. Effects of rotary inertia and other inertias are also included. Efficacy of the present theory is demonstrated through illustrative examples