Identification of Warping Modes of Thin-Walled Beams with Closed Cross-Sections

A simple procedure to identify the warping modes of the thin-walled beam with a closed cross-section is presented. To capture the structural deformation, the displacement field is approximated with the linear combination of basis functions. By means of the free vibration analysis, the participation of each basis function and the mutual interdependency in a modal shape are derived, allowing to assemble them into a reduced set of warping modes with a premise of synchronous vibration along the beam axis. Then the identified warping modes are further hierarchically organized according to the source they are assembled and the sequences they appear in the vibration modes. Finally, these warping modes are used to update the governing equations to form a reduced one-dimensional model. Numerical examples are presented to illustrate the procedure and to verify the ability of the model to capture the warping of thin-walled structures with closed cross-sections.