A Dynamic Stiffness Approach for Vibration Analysis of a Laminated Composite Beam

An exact dynamic stiffness approach for vibration analysis of laminated composite beams with arbitrary ply orientation is introduced in this paper. The influences of Poisson effect, shear deformation and rotary inertia are accounted for in the formulation. The coupled equations of motion are derived first by using the Hamilton principle and the dynamic stiffness matrix is established based on the analytical solutions of the governing differential equations. The automated Muller root search algorithm is then applied to the developed dynamic stiffness matrix to calculate the natural frequencies and mode shapes of the particular composite beams. The influences due to Poisson effect, shear deformation, anisotropy, slenderness ratio and boundary condition on the natural frequencies of the composite beams are investigated. Numerical results of the present method are validated by comparison with those previously published in literature.