Dynamics of thin-walled beams of open section

Abstract

A study of the coupled torsional and bending vibrations of thin-walled beams of asymmetric open section is made. The formal solution to Gere's theory for the case of a monosymmetric section under general loading conditions and boundary conditions is presented. A higher order theory including the effect of shear strain induced by bending and warping of the beam is derived. Spectrum curves of the higher order theory are compared with those from the elementary theory for various boundary conditions for a special family of monosymmetric sections. A study is made to assess the effect of the shape of the cross section of the beam to the differences of the spectrum curves from the two theories. An experiment is performed on two specimens to determine their natural frequencies at different beam lengths and the experimental results are compared to those predicted from the two theories. It is concluded that when the beam is long, the elementary theory is adequate to predict the natural frequencies for torsion predominant modes, but is inadequate for bending predominant modes. For bending predominant modes, the higher order theory should be used. The higher order theory also serves as a guide for the range of validity of the elementary theory. Certain nonlinear behavior of the beam is observed in the experiment. When the beam is excited at resonance at a higher mode, under special circumstances, there is a tendency for the beam to shift from the higher resonant mode to vibrate at its fundamental mode, resulting in a high order subharmonic oscillation. An analysis is made to show the possibility of such behavior if the. inherently nonlinear governing equations for coupled torsional and bending vibrations are used.