Free Vibration Analysis of Composite Laminated Beams

Abstract

This study addresses the problem of free vibration of laminated composite beams. Six end boundary conditions for beams are considered: clamped-clamped; hinged-hinged; free-free; clamped-hinged; clamped-free; and hinged-free beams. The problem is analyzed and solved using the energy approach which is formulated by a finite element model. This method of analysis is verified by comparing the numerical results obtained for AS/3501-6 graphite/epoxy composites with those found in literature. The effects of the aspect ratio, fiber orientation, and the beam end-movements on the non-dimensional natural frequencies of beams were included. The results of the non- dimensional frequencies for some special cases of lamination were included. The mode shapes of free vibration for all boundary conditions were plotted. It was found that symmetrically  and anti-symmetrically  laminated beams of similar dimensions and end conditions have equal natural frequencies. The longitudinal modes of free vibration are sensitive to axial motion of the ends, whereas the transverse modes depend solely on the condition of the lateral supports. It was also found that natural frequencies decrease as the aspect ratio and/or the angle of orientation increase. The free-free and hinged-free beams are found to have the highest frequencies of all beams although they look less constrained.