Page 404 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 12.5 Digital Computer Program for the Torsional System 391

^ j < N . ^ r \ .
/V+2

/v+2 Figure 12.5-1.

Example 12.5-1
Determine the natural frequencies and mode shapes for the torsional system of Fig.
12.5-2.

Figure 12.5-2.

Solution: The frequency range can be scanned by choosing an initial and an increment
Ao). We choose for this problem the frequencies
io = 40, 60,80,..., 620
which can be programmed as

co{I) = 40 + ( / - 1)*20 I = I to 30
The corresponding A(/) is computed as

A(/) =it>(/)**2

The computation is started with the boundary conditions = 1:
S{IA) = 1
r ( / , i ) = A (/)* A/(i)

Equations (12.5-1) and (12.5-2) then give the values of 6 and T at the next station
M = N -\- \ = 2. This loop is repeated until A/ = 4, at which time I is advanced an
integer to the next frequency. The process is then repeated. These operations are
clearly seen in the flow diagram of Fig. 12.5-3.