(a) Find the natural frequencies of the system shown in Fig. 6.31 with \(m_{1}=m_{2}=m_{3}=m\) and \(l_{1}=l_{2}=l_{3}=l_{4}=l / 4\).

(b) Find the natural frequencies of the beam when \(m=10 \mathrm{~kg}, l=0.5 \mathrm{~m}\), the cross section is a solid circular section with diameter \(2.5 \mathrm{~cm}\), and the material is steel.

(c) Consider using a hollow circular, solid rectangular, or hollow rectangular cross section for the beam to achieve the same natural frequencies as in (b). Identify the cross section corresponding to the least weight of the beam.

Figure 6.31:-

Transcribed Image Text:

4- m m2 m3 FIGURE 6.31 Fixed-fixed beam carrying three masses.