Flutter Instability of Timoshenko Cantilever Beam

This paper presents effect of shear deformation on flutter instability of cantilever beam subjected to a concentrated follower force. The equation of motion in matrix form is formulated based on the Lagrange approach and the finite element method. 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 has significant increases 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 considering the Timoshenko beam on the accuracy ofthe analysis for different beam thicknesses.

Keywords:

Flutter instability , Non conservative force , Timoshenko beam , Finite element method