A uniform shaft carries three rotors as shown in Fig. 7.18 with mass moments of inertia \(J_{1}=5 \mathrm{~kg}-\mathrm{m}^{2}, J_{2}=15 \mathrm{~kg}-\mathrm{m}^{2}\) and \(J_{3}=25 \mathrm{~kg}-\mathrm{m}^{2}\). The torsional stiffnesses of the segments between the rotors are given by \(k_{t 1}=20,000 \mathrm{~N}-\mathrm{m} / \mathrm{rad}\) and \(k_{t 2}=60,000 \mathrm{~N}-\mathrm{m} / \mathrm{rad}\). Determine the natural frequencies and mode shapes of the system using Holzer's method.

Figure 7.18:-

Transcribed Image Text:

J Kn Jo FIGURE 7.18 Shaft carrying three rotors. J3 K12