7th International Conference on Vibration Problems (ICOVP 2005), İstanbul, Turkey, 5 - 09 September 2005, vol.111, pp.531-536
As is well known, there are the first and higher order shear deformation theories that involve the shear correction factor (k- factor), which appears as a coefficient in the expression for the transverse shear stress resultant, to consider the shear deformation effects with a good approximation as a result of non-uniform distribution of the shear stresses over the cross-section of the beam. Timoshenko's beam theory (TBT) accounts both the shear and rotatory inertia effects based upon the first order shear deformation theory which offers the simple and acceptable solutions. The numerical value of the k- factor which was originally proposed by Timoshenko depends upon generally both the Poisson's ratio of the material and the shape of the cross-section. Recently, especially the numerical value of the k-factor for rectangular sections is examined by both theoretical and experimental manners. Although there are no large numerical differences among the most of the theories, a few of them says that the k-factor varies obviously with the aspect ratio of rectangular sections while Timoshenko's k-factor is applicable for small aspect ratios. In this study, the effect of the different k-factors developed by Timoshenko, Cowper and Hutchinson on the in-plane free vibration of the orthotropic beams with different boundary conditions and different aspect ratios are studied numerically based on the transfer matrix method. For the first six frequencies, the relative differences of among the theories are presented by charts.