Transient vibrations of a cantilever beam rotating at a constant angular acceleration

Abstract

A method for determining the transient vibrational effects produced by application of a constant angular acceleration to a cantilever beam initially at rest was determined. This method is applicable to beams of uniform cross-sectional area vibrating in their planes of rotation. The governing differential equations include the effects of bending, shear deformation and rotary inertia. Coriolis' acceleration, however, is neglected.

These governing equations were non-dimensionalized and solved by numerical means using a finite difference approach and dividing the beam's length into 12 sections, since their complexity made an exact solution appear impossible. This was done by the aid of a 1620 I.B.M. Computer.

Application of this solution to an actual beam indicated that a wave propagation type of response becomes more clearly evident as the hub radius is increased. The numerical results also indicate that the initial displacements are a direct result of shear deformation.

The effect of centrifugal force was also analyzed. At large values of time this force caused the beam to return to its undeformed axis.

Solutions for a short time interval extending over 1100 steps, a large time interval extending over 275 steps, and another using the short time interval together with a reduced radius, 250 steps, were obtained.