Free Vibration Of Nonsymmetrical Thin Walled Beams

Abstract

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.