A DYNAMIC FINITE ELEMENT (DFE) APPROACH FOR COUPLED BENDING-TORSIONAL VIBRATIONS OF BEAMS

A new Dynamic Finite Element (DFE) formulation for the coupled bending-torsion vibrational analysis of uniform beams is presented. The frequency dependent trigonometric shape functions, corresponding to the uncoupled bending and torsional vibrations, are used to find the elementary stiffness matrix which has both mass and stiffness properties. The implementation of the derived DFE matrix in a program is discussed with particular reference to an established algorithm. Within the limits of this method, an approach to calculate the number of constrained frequencies of a member, lying between zero and any trial frequency, is also presented. This enable coupled vibration analysis of beams, or assemblages of coupled beams, to be made. The application of the theory is demonstrated by three illustrative examples of wings of different configurations wherein a substantial amount of coupling between bending and torsion is highlighted. The correctness of the theory is confirmed, to a high degree of accuracy, by published results and numerical checks.