Accelerating Load on a Rotating Rayleigh Beam

The response of a rotating Rayleigh beam subjected to an axially accelerated distributed surface line load is studied. Clamped-clamped, clamped-pinned, and clamped-free support conditions and four types of load velocity profiles are treated. Galerkin's method is used to suppress spatial dependence in the equations of motion; the resulting time dependent equations are numerically integrated. Results are presented for the beam displacement in the direction of the load and the gyroscopically induced transverse component. The effects of load speed, beam rotational speed, and geometry are studied, the potential for control of the beam vibrations by adjustment of the load velocity profile is discussed.