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 be ams is studied by the transfer matrix method. The distributed parameter mod el is used for predicting the natural frequencies. The rotary inertia and s hear deformation effects are considered in the Timoshenko beam analysis bas ed on the first-order shear deformation theory. For the Bernoulli-Euler bea m analysis, these effects are neglected to study the effects of shear defor mation and rotary inertia on the first six natural frequencies. The numeric al algorithm available in the literature is used to compute the exact overa ll dynamic transfer matrix. The effects of the rotary inertia and shear def ormation are investigated for length/thickness ratios from 3 to 20, fixed-f ixed, fixed-simple and fixed-free boundary conditions, and two values of th e thickness/width ratios of rectangular section (2, 0.5). The results obtai ned by the Bernoulli-Euler and Timoshenko beam theories and relative errors between the two theories are presented in graphical form. (C) 2000 Elsevie r Science Ltd. All rights reserved.