Axial Static Force Effect on Coupled Torsional-Warping Vibration for Thin-Walled I-Beams Subjected to Harmonic Torsional Moments

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Mohammed Ali Hjaji Neffati M. Werfalli


An exact closed form solution is developed for the coupled torsional-warping vibration response of thin-walled open doubly symmetric I-beams subjected to various dynamic torsional moment excitations and axial constant static force. Based on a Vlasov-Timoshenko beam theory, the governing differential equations and associated boundary conditions for coupled torsional-warping vibration are derived from Hamilton’s variational principle. The present exact formulation accounts for shear deformation, effects due to non-uniform warping and axial constant static forces. The resulting coupled equations for thin-walled beams are exactly solved and the exact closed form solutions for steady state torsional-warping dynamic response are then obtained for cantilever and simply supported boundary conditions. The applicability of the exact closed-form solutions are demonstrated via several examples with various torsional harmonic loads and boundary conditions and by including and excluding the axial static force effects. Results based on the present exact formulation are assessed and validated against other well established ABSQUS finite element and Galerkin-based finite beam element solutions.


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