摘要：Thin walled and open section beams are extensively used as structural components in different structures in Civil, Aeronautical and Mechanical Engineering fields. Free vibrations of doubly symmetrical beams or beams with one axis of symmetry are widely studied, in general by using Bernoulli-Navier theory. However, results about doubly unsymmetrical beams are rather limited. In this case, triple coupled flexural-torsional vibrations are observed. In this paper, a numerical study is presented about natural frequencies of doubly unsymmetrical thin-walled and open cross-section beams. The equations of motion are based on Vlasov's 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 discussion related to vibration of unsymmetrical channel cross-section beams is presented. In this sense, relevant topics discussed in recent works are pointed out.
