The effect of a concentrated mass on the modal characteristics of a rotating cantilever beam

Modal characteristics of rotating cantilever beams with a concentrated mass located in an arbitrary position are investigated in this paper. Equations of motion are derived by employing hybrid deformation variables. The resulting equations are linear but capture the stiffening effect induced by the rotational motion of the beam. For modelling of the concentrated mass, use is made of the Dirac delta function, which avoids increasing the degrees of freedom of the system. The resulting equations of motion are transformed into dimensionless forms in which four dimensionless parameters are identified. The effects of the dimensionless parameters on the modal characteristics of the rotating beams are examined through numerical study. It is found that the magnitude and the location of the concentrated mass significantly influence the modal characteristics of the rotating beam.