Page 402 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 12.4 Holzer Method 389

TABLE 12.4-1
Parameters of the System
Station 1 Station 2 Station 3

7, = 5 72 = 11 = 22
a:, = 0.10 X 10'' a:, = 0.20 X 10'’ K2 = 0
Calculation Program
OJ 0, == 1.0 02 = 1 - T^/k, 0, = 02 - T^/kj

0)^ r, = T2 —Tj 0)^6 2J1 T = T2 +

20 1.0 0.980 0.9484
400 2.0 X IO"* 6.312 X 10-' 14.66 X 10-'
'

40 1.0 0.920 0.799
1600 8.0 X lO"* 24.19 X 10-^ 52.32 X 10-'

Solution: Table 12.4-1 defines the parameters of the system and the sequence of calcula­
tions, which can be easily carried out on any programmable calculator. Presented are
calculations for co = 20 and 40. The quantity is the torque to the right of disk 3,
which must be zero at the natural frequencies. Figure 12.4-3 shows a plot of versus
0). Several frequencies in the vicinity of = 0 were inputted to obtain accurate
values of the first and second mode shapes displayed in Fig. 12.4-4.

wu

Figure 12.4-3.