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 t aken to be deflection dependent: that is, to vary according to the def lection of the beam at the contact center; superposed harmonic time de pendence is also included. The Timoshenko beam model incorporating gyr oscopic effects is used. Two types of load velocity profiles are consi dered, along with clamped-clamped and pinned-pinned support conditions . Spatial dependence in the beam's governing equations of motion is sa tisfied using Galerkin's method. The resulting time dependent equation s are numerically integrated for the transient response of the beam at the load contact center for a variety of cases. Conditions under whic h the moving force excites the beam into resonance are derived in the general case of load deflection dependence with superposed harmonic de pendence. These conditions are found to involve load speed, the freque ncy of the superposed time dependence, cutting parameters and the beam properties. Resonance plots are presented for a variety of cases.