A Dynamic Finite Element (DFE) for coupled bending-torsional vibrations of axially loaded beams

摘要

A Dynamic Finite Element (DFE) formulation for coupled bending-torsional free vibrations of axially loaded beams is presented. ^Analytical expressions of uncoupled bending and torsional dynamic shape functions of an axially loaded uniform beam element, derived in an exact sense, are used to obtain the frequency dependent stiffness matrix corresponding to the coupled vibration of this type of beam element. ^It leads to an expression for the clamped-clamped natural frequencies which has also been investigated. ^The influence of the axial force on the coupled bending-torsional frequencies of a cantilever beam of thin-walled section is demonstrated by numerical results. ^Application of the developed theory includes frequency and mode calculations of helicopter, turbine and propeller blades, plane and space frames, and grillage consisting of axially loaded beam elements with noncoincident mass and shear center. ^(Author)