A steel shaft of diameter \(d\) and length \(l\) is fixed at one end and carries a propeller of mass \(m\) and mass moment of inertia \(J_{0}\) at the other end (Fig. 8.30). Determine the fundamental natural frequency of vibration of the shaft in (a) axial vibration, and (b) torsional vibration. Data: \(d=5 \mathrm{~cm}, l=1 \mathrm{~m}, m=100 \mathrm{~kg}, J_{0}=10 \mathrm{~kg}-\mathrm{m}^{2}\).

Transcribed Image Text:

Propeller; mass m, mass moment of inertia Jo d x+ FIGURE 8.30 Shaft connected to a propeller.