COUPLED BENDING-TORSIONAL VIBRATIONS OF ASYMMETRICAL BERNOULLI-EULER THIN-WALLED BEAM

The exact dynamic transfer matrix is derived for a straight and uniform Bernoulli-Euler thin-walled beam element whose elastic and inertial axes are not coincident by directly solving the governing differential equations of motion of the beam. The Bernoulli-Euler bending-torsion coupled beam theory is used, and the cross-section is asymmetric. The bending vibrations in two perpendicular directions are coupled with torsional vibration and the effect of warping stiffness is included. The dynamic transfer matrix can be used for calculation of exact natural frequencies and mode shapes for asymmetrical thin-walled beams and its assemblages. Numerical results are given for an example of thin-walled beam with a variety of boundary conditions, and numerical solutions of natural frequencies are tabulated for comparison. The effect of warping stiffness on natural frequencies and mode shapes is also discussed. The results show that when the warping effect is neglected, the associated errors become increasingly large as the frequency order increases.