A Dynamic Finite Element (DFE) method for free vibrations of bending-torsion coupled beams

In this paper, a Dynamic Finite Element (DFE) formulation for the free vibr ation analysis of bending-torsion coupled beams is presented. First, the ex act solutions of the differential equations governing the uncoupled vibrati ons of a uniform beam are found. The employment of these solutions as basis functions leads to the appropriate frequency dependent shape functions whi ch can then be utilized to find the nodal approximations of variables. By e xploiting the Principle of Virtual Work (PVW), the elementary Dynamic Stiff ness Matrix (DSM) is then obtained which has both mass and stiffness proper ties. The implementation of the derived DFE matrices in a program is discus sed with a particular reference to the Wittrick-Williams algorithm. The app lication of the theory is demonstrated by illustrative examples wherein a s ubstantial amount of coupling between bending and torsion is highlighted. T he correctness of the theory is confirmed, to a high degree of accuracy, by published results and numerical checks. (C) 2000 Editions scientifiques et medicales Elsevier SAS.