A New Beam Finite Element with Seven Degrees of Freedom at Each Node for the Study of Coupled Bending-Torsion Vibrations
NATIONAL INST OF APPLIED SCIENCES TOULOUSE (FRANCE)
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The subject matter of the first part of this study is the derivation of coupled bending-torsion relations characterizing the dynamical behaviour of unsymmetrical cross-section beams. This allows for the further definition of a beam element with seven degrees of freedom per node. The numerical results obtained with the FEM are compared to experiment in some section shape cases. In order to characterize the displacement field of considered beams, the method of integrated displacements allows us to consider the so-called secondary effects longitudinal warping inertia, and shear deformation due to both shearing forces and nonuniform warping. The literature on dynamical flexure and torsion of beams is extensive. Cowper for flexure and Gay-Boudet for torsion introduce integrated displacements. We extend in the following this notion to the study of coupled bending-torsion of an homogeneous straight beam.