A SPINNING BEAM SUBJECTED TO A MOVING DEFLECTION DEPENDENT LOAD .2. PARAMETRIC RESONANCE

The parametric resonance of a spinning Timoshenko beam is studied for pinned and clamped supports. Axially moving loading, which is deflecti on dependent and contains superposed harmonic time dependence, is appl ied to the beam. The deflection dependent nature of the loading produc es time dependent coefficients in the governing equations and hence th e possibility of parametric resonance when the time dependence is peri odic. Dynamic instability diagrams are determined by the monodromy mat rix method for various load cases. Instability regions are found which emanate from the beam's forward and backward precession natural frequ encies and from various combinations of these frequencies. It is concl uded that the Euler-Bernoulli theory may underestimate the level of po ssible instability in a rotating beam.