A. Argento et Hl. Morano, A SPINNING BEAM SUBJECTED TO A MOVING DEFLECTION DEPENDENT LOAD .2. PARAMETRIC RESONANCE, Journal of sound and vibration, 182(4), 1995, pp. 617-622
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.