Coupled Vibrations of Thin-Walled Elastic Bars

A study of the coupled torsional and bending vibrations of thin-walled beams of asymmetric open section is made. The validity of existing theories has been examined both analytically and experimentally. Analytically, a higher order theory that includes effects of shear strains induced by bending and warping was constructed and compared with the existing elementary theory for five different boundary conditions. Experimentally, tests were conducted on beams of two different cross sections of various lengths. The resonant frequencies were found and compared with the values predicted from theoretical calculations. It is concluded that when the beam is long, the elementary theory is adequate to predict the natural frequencies for the first few torsion predominant modes, but is inadequate for bending predominant modes. For bending predominant modes, the higher order theory should be used. Also, the higher order theory serves as a guide for the range of validity of the elementary theory.