Page 429 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

416 Classical Methods Chap. 12

12-37 A torsional system with a torsional damper is shown in Fig. P12-37. Determine the
torque-frequeney curve for the system.

g, = lO-*

^2 = 100 Figure P12-37.
12-38 Determine the equivalent torsional system for the geared system shown in Fig. PI2-38
and find its natural frequency.

d, = l | 1, = 40'
^ 3" dia-
6 diQ.
= 10 Ib-in.-s2
Md2-2 12=30"
J2 = 24 Figure P12-38.
12-39 If the small and large gears of Prob. 12-38 have the inertias J' = 2 and J”= 6,

determine the equivalent single shaft system and establish the natural frequencies.
12-40 Determine the two lowest natural frequencies of the torsional system shown in Fig.
PI2-40 for the following values of 7, K, and n

7j = 15 lb ' in.• s^
K^ = 2X 10^ lb • in./rad
J2 = 101b • in. - s^

K^ = 1.6 X 10^ lb • in./rad
73 = 18 1b • in. - s^
7^3 = 1 X 10^ lb - in./rad

74 = 6 lb - in. - s^
K^ = 4X 10^ lb - in./rad
Speed ratio of the drive shaft to axle = 4 to 1
What are the amplitude ratios of J2 to 7j at the natural frequencies?