The vibration behaviour of thin-walled regular polygonal tubes

• The undamped free vibration behaviour of polygonal tubes is presented.
• Local, extensional, distortional, torsional and multi-mode vibration modes are investigated.
• Numerical and analytical closed-form solutions are presented.
• Duplicate vibration modes are obtained in some cases.

This paper addresses the free vibration behaviour of single-cell thin-walled tubes with regular convex polygonal cross-section (RCPS) and provides an extensive analysis of the resulting natural frequencies and associated vibration mode shapes. A semi-analytical approach is adopted, which is based on the generalised beam theory (GBT) specialisation for RCPS recently proposed by Gonçalves and Camotim (2013) [1] and subsequently employed to obtain insightful conclusions concerning the buckling behaviour of RCPS tubes (Gonçalves and Camotim (2013) [2] and [3]). This approach makes it possible to obtain closed-form analytical solutions and also acquire in-depth knowledge concerning the mechanics of the vibration problem, through the well-known GBT modal decomposition features. Attention is paid to local (plate-like), extensional, torsional and distortional vibration modes, as well as their interaction.