Free Vibration Of Nonsymmetrical Thin Walled Beams. Numerical-Experimental Comparison.

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-experimental comparison 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 and
clarified. Experimental tests about these unsymmetrical beams are presented which allow
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.