Effects of axial movements of the ends and aspect ratio of laminated composite beams on their non-dimensional natural frequencies

Abstract

This study developed to solve the problem of prediction of the natural frequencies of free vibration for laminated beams. The study presented the natural frequencies of composite beams with four layered and different boundary conditions. In each boundary condition, two cases are assumed: movable ends and immovable ends. Numerical results are obtained for the same material to demonstrate the effects of the aspect ratio, fiber orientation, and the beam end-movements on the non-dimensional natural frequencies of beams. Two aspect ratios are given in the numerical results, one is for relatively short-thick beams, while the other is for slender beams. It was found that the results of the non-dimensional frequencies obtained from the short-thick beams are generally much less than those obtained from the other slender beams for same fiber orientation and generally, the frequencies of longitudinal vibration increase as the aspect ratio increased. It was also found the values of the non-dimensional frequencies of the transverse modes are not affected by the longitudinal movements of the ends since these modes are generated by lateral movements only. However, 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.