Finite element modelling of the coupled bending and torsional free vibration of uniform beams with an arbitrary cross-section

The coupled bending and torsional natural frequencies of uniform elastic beams with arbitrary cross-section are studied using the finite element method. The special cases of cross-sectional symmetry in one or two perpendicular direction and negligible warping and rotary inertia effects can be treated readily by simply removing some of the entries of stiffness and mass matrices. Coupled natural frequencies of asymmetric and monosymmetric beams are obtained for a variety of classical boundary conditions, and a reasonably good agreement has been achieved with the exact results published in the literature. (C) 1997 by Elsevier Science Inc.