Elasticity-based free vibration of anisotropic thin-walled beams

• We study the free vibration of thin-walled beams.
• Beams with both open and closed section are considered.
• Three-dimensional elasticity theory is used rather than more common beam theories.
• We compare results with recent studies that have divergent results.

The free-vibration of anisotropic open and closed thin-walled beams is studied using approximate solutions to the three-dimensional equations of motion of a linear elastic solid. The three displacement components are approximated using grouped polynomials over both the cross-section coordinates and independent polynomial or trigonometric functions over the axial coordinate of several beams with representative boundary conditions. This method is applied to several sections with varying degrees of anisotropy and shape with both isotropic and orthotropic material properties. Results are compared with those computing using beam or shell theories, and several new results are presented for these geometries.