Consider the model of a bladed disk (Sinha, 1986) shown in Figure P5.1 where each blade is represented by a single mass. Furthermore, it should be noted that \(i+1=1\) when \(i=N\) and \(i-1=N\) when \(i=1\), where \(N\) is the number of blades. Model parameters are as follows: \(m_{t}=0.0114 \mathrm{~kg}, k_{t}=430,000 \mathrm{~N} / \mathrm{m}\), and \(K_{c}=45,430 \mathrm{~N} / \mathrm{m}\).

Figure P5.1 

a. Compute the natural frequencies and the mode shapes when \(N=3\). Examine the orthogonality of the mode shapes.

b. Compute the natural frequencies and the mode shapes when \(N=10\). Examine the orthogonality of the mode shapes.

Transcribed Image Text:

X-1 1x x+1 K m Kc FM k K m WW m WH k W... W k