SPINNING BEAM SUBJECTED TO A MOVING DEFLECTION DEPENDENT LOAD .1. RESPONSE AND RESONANCE

The response and resonance of a rotating beam subjected to an axially accelerating distributed line load is studied. The load magnitude is taken to be deflection dependent: that is, to vary according to the deflection of the beam at the contact center; superposed harmonic time dependence is also included. The Timoshenko beam model incorporating gyroscopic effects is used. Two types of load velocity profiles are considered, along with clamped-clamped and pinned-pinned support conditions. Spatial dependence in the beam's governing equations of motion is satisfied using Galerkin's method. The resulting time dependent equations are numerically integrated for the transient response of the beam at the load contact center for a variety of cases. Conditions under which the moving force excites the beam into resonance are derived in the general case of load deflection dependence with superposed harmonic dependence. These conditions are found to involve load speed, the frequency of the superposed time dependence, cutting parameters and the beam properties. Resonance plots are presented for a variety of cases.