Demonstrate how rapidly Rayleigh’s method converges for the uniform-diameter solid shaft of Prob. 7–28, by partitioning the shaft into first one, then two, and finally three elements.
Prob. 7–28, A 25-mm-diameter uniform steel shaft is 600 mm long between bearings.
(a) Find the lowest critical speed of the shaft.
(b) If the goal is to double the critical speed, find the new diameter.
(c) A half-size model of the original shaft has what critical speed?