Effect of the longitudinal to transverse moduli ratio on the in-plane natural frequencies of symmetric cross-ply laminated beams by the stiffness method

In this study, the stiffness method is used for the solution of the purely in-plane free vibration problem of symmetric cross-ply laminated beams. The rotary inertia, axial and transverse shear deformation effects are conside red in the mathematical model by the first-order shear deformation theory. A total of six degrees of freedom, four displacements and two rotations are defined for an element. The exact in-plane clement stiffness matrix of 6 x 6 is obtained based on the transfer matrix method. The element inertia mat rix consists of the concentrated masses. The sub-space iteration and Jacobi 's methods are employed in the solution of the large-scale general eigenval ue problem. After verifying the accuracy of the present formulation, the in -plane mode shapes associated with the first eight natural frequencies of t he vibrating beam with fixed-free. fixed-simple, and fixed-fixed boundary c onditions are illustrated. Finally, the effect of the longitudinal to trans verse moduli ratio on the first three in-plane natural frequencies is inves tigated for different length/thickness ratios (5 and 20) and boundary condi tions (fitted-free and fixed-fixed). (C) 2000 Elsevier Science Ltd. All rig hts reserved.