Investigation of the rotary inertia and shear deformation effects on the out-of-plane bending and torsional natural frequencies of laminated beams

The out-of-plane free vibration problem of symmetric cross-ply laminated beams is studied by the transfer matrix method. The distributed parameter model is used for predicting the natural frequencies. The rotary inertia and shear deformation effects are considered in the Timoshenko beam analysis based on the first-order shear deformation theory. For the Bernoulli-Euler beam analysis, these effects are neglected to study the effects of shear deformation and rotary inertia on the first six natural frequencies. The numerical algorithm available in the literature is used to compute the exact overall dynamic transfer matrix. The effects of the rotary inertia and shear deformation are investigated for length/thickness ratios from 3 to 20, fixed-fixed, fixed-simple and fixed-free boundary conditions, and two values of the thickness/width ratios of rectangular section (2, 0.5). The results obtained by the Bernoulli-Euler and Timoshenko beam theories and relative errors between the two theories are presented in graphical form. (C) 2000 Elsevier Science Ltd. All rights reserved.