Dynamic analysis of laminated composite beams using higher order theories and finite elements

Free vibration analysis of laminated composite beams is carried out using two higher order displacement based shear deformation theories and finite elements based on the theories. Both theories assume a quintic and quartic variation of in-plane and transverse displacements in the thickness coordinates of the beams respectively and satisfy the zero transverse shear strain/stress conditions at the top and bottom surfaces of the beams. The difference between the two theories is that the first theory assumes a non-parabolic variation of transverse shear stress across the thickness of the beams whereas the second theory assumes a parabolic variation. The equations of motion are derived using Hamilton’s principle. Further two-node C1 finite elements of eight degrees of freedom per node, based on the theories, are presented for the free vibration analysis of the beams in this paper. Numerical results have been computed for various length to thickness ratios and for various boundary conditions of the beams and compared with the results of other theories and finite elements available in literature. The comparison study shows that the theories and the finite elements predict the natural frequencies of the laminated composite beams better than the other theories and the finite elements considered.