Effect of static large deformation on dynamic characteristic of a beam

Based on Timoshenko beam theory, the new tangent stiffness is derived by introducing warping modification coefficient and using Updated Lagrangian formulation. A model for its static and dynamic analysis of a large deformation spatial beam is developed, based on the virtual work increment equation for three-dimensional continuum, considering effect of shearing and warping deformations. Firstly, According to the analytical model obtained, several numerical tests are performed to verify the effectiveness of the finite element model of a special beam subjected to tip loading. The first two examples show how the present formulation models the large deformation spatial beam and the model is correct. Secondly, its dynamic deformation behavior is investigated to show affection of static deformation on dynamic deformation. The results reveal that the natural frequencies are evidently changed as a large tip loading is applied on a cantilever beam, especially for its fundamental natural frequency.