On free vibration of nonsymmetrical thin-walled beams

In this paper, a numerical–experimental study about natural frequencies of doubly unsymmetrical thin-walled and open cross-section beams is presented. The equations of motion are based on Vlasovʹs theory of thin-walled beams, which is modified to include the effects of shear flexibility, rotatory inertia in the stress resultants and variable cross-sectional properties. The formulation is also applicable to solid beams, constituting therefore a general theory of coupled flexure and torsion of straight beams. The differential equations are shown to be particularly suitable for analysis in the frequency domain using a state variables approach. A simplified theory, which excludes the analysis the warping constraint, is presented leading to a more simple theory that is used for comparison purposes in this paper. Finally, free vibration experimental tests about unsymmetrical beams are presented which allow to verify the theory presented in this paper and provide good quality data that can be used for checking the accuracy and reliability of different theories.