ABSTRACT
Consider a rod attached to a thin shaft rotating steadily at angular velocity ω (see Figure 12.1), with f0=0.
If r is the undeformed position along the shaft, the governing equation is
(12.5)
Assuming a one-element model with u(r, t)=ru(L, t)/L, we obtain
(12.6)
Clearly, u(L, t) becomes unbounded if ω becomes equal to the natural frequency
in which case, ω is called a critical speed.
