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

Abstract

In this paper, variationally consistent layer-wise trigonometric shear deformation theory (LTSDT) has been extended to deal with free vibration of two-layered laminated cross-ply beams. In this displacement based theory, constitutive relations between shear-stresses and shear-strains are satisfied in both the layers, and, therefore, shear correction factor is not required. In-plane displacement is such that the resultant of normal stress acting over the cross section is zero. Compatibility at the layer interface in respect of in-plane displacement is also satisfied. Present theory contains even less number of unknown variables than those of the first order shear deformation theory (FSDT). In the present formulation, effects of rotary inertia and other inertias are also included. The efficacy of the present theory is demonstrated through the illustrative example.