Comparison of the In-Plane Natural Frequencies of Symmetric Cross-Ply Laminated Beams Based on the Bernoulli-Euler and Timoshenko Beam Theories

Abstract

The in-plane free vibration problem of symmetric cross-ply laminated beams is studied based on the transfer matrix method. Distributed parameter model is used in the mathematical formulation. The rotary inertia, the shear and extensional deformation effects, are considered for the Timoshenko’s beam analysis. These effects are neglected in the Bernoulli-Euler analysis. The exact overall dynamic transfer matrix of the beam is obtained by making use of the numerical algorithm available in the literature. In order to obtain detailed knowledge about the effects of the rotary inertia, shear and axial deformations on the first six non-dimensional frequencies, the results of Timoshenko and Bernoulli-Euler theories are compared with each other for length-to-thickness ratios from ranging 3 to 20. Fixed-fixed, fixed-simple, and fixed-free boundary conditions are considered for three values of the thickness-to-width ratios of a rectangular section (2, 1, 0.5).