Effect of Transverse Shear on Flutter Instability of a Timoshenko Free-Free Beam Under Non-conservative Axial Force

effect of shear deformation on flutter instability of free-free beam subjected to a concentrated follower force is investigated in this paper. The equation of motion in matrix form is formulated based on the Lagrange approach and FEM is used. In the presented method, FEM is developed in context of Timoshenko beam theory which accounts for constant shear distribution through the thickness of the beam. Moreover the effect of rotary inertial term has been considered which makes significant increase with thickness. Consistent interpolation scheme is adopted to avoid the shear locking for thin beams. In addition, convergence of the finite element simulation is enhanced. Results are presented for different conditions of beams. The numerical results show high efficiency and good convergence characteristics. Furthermore, the Euler beam theory is also used to investigate the effects of assuming the Timoshenko beam on the accuracy of the analysis for different beam thicknesses

Keywords:

Flutter instability , free-free beam , Non-conservative force , Timoshenko beam , Finite element method.