A Dynamic Finite Element for the Free Vibration Analysis of Nonuniform Extension-Torsion Coupled Composite Box-Beams

The extension-torsion coupled vibration of composite box-beams is revisited. A semi-analytical Refined Dynamic Finite Elements (RDFE) modal analysis method is presented and compared with the other well established methods, such as exact Dynamic Stiffness Matrix (DSM) and conventional FEM formulations. The beam thin-walled closed section is assumed to be a Circumferentially Uniform Stiffness (CUS) configuration, where torsional displacement is assumed to be governed by St. Venant theory. The hybrid DFE method is achieved by combining the classical FEM and ‘exact’ Dynamic Stiffness Matrix (DSM) theories. The approximation space is defined using frequency-dependent trigonometric basis functions to obtain the corresponding Dynamic Interpolation Functions (DIFs). Application of the weighted residual method to the differential equations of motion and discretizing the integral form of the equations of motion, where the approximate field variables are expressed in terms of the DIFs, then leads to the DFE element stiffness matrices. Effects of variable geometric and material properties are included in the DFE matrices through ‘deviatoric terms’, to further refine the formulation. The Wittrick-Williams (WW) algorithm is used to calculate the structural natural frequencies and modes for illustrative examples, and tested against conventional FEM and DSM formulations. The RDFE is shown to be a highly convergent tool for structural vibration analysis.