Dynamic stability of a radially rotating beam subjected to base excitation

The equations of motion of a rotating cantilever beam subjected to base excitation are derived using the Euler beam theory and the assumed mode method. The coefficients of the resulting equations of motion are found to have two distinct and independent frequencies. One of them is the base excitation frequency while the other corresponds to that of the angular velocity. This form of equation is different from the standard Mathieu-Hill's equations and has not been analysed in the literature. This coupled set of equations of motion is then uncoupled and the multiple scale method is used to determine the instability boundaries of the system. Numerical results are presented to illustrate the influence of the hub radius to length of beam ratio, steady state rotating speed and base excitation frequency on the dynamic stability of the system. Dynamic instability due to various combination resonances were examined.