Free vibration analysis of the laminated composite beam with various boundary conditions.

Abstract

A dynamic finite element approach for free vibration analysis of generally laminated composite beams is introduced on the basis of first order shear deformation theory. The effect of Poisson effect, bending and torsional deformations, couplings among extensional, shear deformation and rotary inertia are comprised in the formulation. The dynamic stiffness matrix is defined based on the exact solutions of the differential equations of motion governing the free vibration of generally laminated composite beam. The influences of Poisson effect, material anisotropy, slender ratio, shear deformation and boundary condition on the natural frequencies of the composite beams are analyze in detail by specific carefully favored examples. The natural frequencies and mode shapes of numerical results are presented and, whenever possible, compared to those previously published solutions in order to describe the correctness and accuracy of the present approach.Free vibration analysis of laminated composite beams is carried out using higher order shear deformation theory. Two-node, finite elements of eight degrees of freedom per node, based on the theories, are presented for the free vibration analysis of the laminated composite beams in this project work. Numerical results have been computed for various ply orientation sequence and number of layers and for various boundary conditions of the laminated composite beams and compared with the results of other higher order theories available in literature. The comparison study shows that the present considered higher order shear deformation theory forecast the natural frequencies of the laminated composite beams better than the other higher order theories considered.For considered examples, the coding of the formulation of first order shear deformation theory and higher order shear deformation theory (two-node , finite elements of eight degree of freedom per node) done by the help of MATLAB and ANSYS 12 software package.Keywords: - shear deformation, slender ratio, natural frequencies, higher order shear deformation theory, laminated composite beam and free vibration.