Effects of Boundary Conditions on Cross-Ply Laminated Composite Beams

Abstract

 In this study, the effect of the end conditions of cross-ply laminated composite beams (CLCB) on their non-dimensional natural frequencies of free vibration was investigated. The problem is analyzed and solved using the energy approach which is formulated by a finite element model. In that model, a three-noded element with three degrees of freedom at each node is assumed. Numerical results were verified by comparisons with other relevant works. The end conditions of beams are: clamped -free (CF), hinged -hinged (HH), clamped -clamped (CC), hinged -clamped (HC), hinged -free (HF), free -free (FF). Each beam has either movable ends or immovable ends. It is found that the more constrained beams have the higher values of natural frequencies of transverse vibration. However, the free-free and hinged-free beams are found to have the highest frequencies of transverse vibration amongst all beams although they look less constrained. This behavior is due to the fact that the first mode of the two beams is equal zero (rigid body motion), and replaced by the second mode to be the fundamental mode. The values of the natural frequencies of longitudinal modes are found to be the same for all beams with movable ends since they are generated by longitudinal movements only. But for immovable ends, the clamped-free and hinged-free beams have equal frequencies in longitudinal vibration, and those of the other beams are also the same.