Free vibration of curved thin-walled rectangular beams

A finite element is presented for the spatial free vibration analysis of horizontally curved thin-walled rectangular box beams. Generalised displacements and generalised coordinates are constructed in accordance with the nine identified cross-section deformation modes, and are employed to formulate the mid-surface contour displacement field. Considering the force-equilibrium condition and the displacement-continuity condition, two different three-dimensional displacement fields of an arbitrary point on the beam are built and used to calculate the strain energy and the kinetic energy of the beam, respectively. With the application of Hamilton's principle, the dynamic equations of the beam are derived; the beam is then approximated with a C0 continuous interpolation function for the finite-element implementation. The validity of this study is confirmed both by the published literature and by Ansys shell theory.