Theoretical and Simulation Finite Element Modal Analysis of Rotating Cantilever Beam

The finite element method is used to carry out modal analysis of rotating cantilever beam. The virtual work method is then used to derive the stiffness matrix of a rotating beam element. The stiffness matrix of a rotating beam element is simply seen to be sum of the stiffness matrix of the non-rotating beam and an incremental stiffness matrix induced by rotation. This work presents a novel generalized incremental stiffness matrix that takes care of any element at any distance from the rotation axis. The established rotational stiffness matrix is then used together with consistent mass matrix (not affected by rotation) to carry out modal analysis of rotating cantilever beam. Theoretical computations were validated by simulations from ANSYS. It is seen that the contribution to modal frequencies and shapes of the blade of rotation via incremental stiffness matrix is very marginal at low rotational speeds. For example it is seen for a numerical case study that five-element model computes slight increase in fundamental natural frequency due to rotation relative to that of the non-rotating blade as 0.000195% for rotational speed of 300rpm. It is also seen that ten times increase in speed leads to about hundred times increase in rotational contribution meaning that it becomes more imperative to model rotation as speed of the blade increases. Points are also made regarding application to avoiding resonance of rotating cantilever beam.