Design the cantilever beam supporting the hoisting drum and the wire rope carrying the load in Problem 5.24 in order to have the natural frequencies of the system greater than \(10 \mathrm{~Hz}\) when \(W_{1}=5000 \mathrm{~N}\) and \(W_{2}=2500 \mathrm{~N}, b=0.75 \mathrm{~m}\), and \(l=1.5 \mathrm{~m}\).

Data From Problem 5.24:-

A hoisting drum, having a weight \(W_{1}\), is mounted at the end of a steel cantilever beam of thickness \(t\), width \(a\), and length \(b\), as shown in Fig. 5.34. The wire rope is made of steel and has a diameter of \(d\) and a suspended length of \(l\). If the load hanging at the end of the rope is \(W_{2}\), derive expressions for the natural frequencies of the system.

Transcribed Image Text:

b (a) FIGURE 5.34 Hoisting drum. W N W ka W2 (b)