Page 430 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 12 Problems 417

i r ^

L hm
Jp Figure P12-40.
12-41 Reduce the torsional system of the automobile shown in Fig. P12-41(a) to the
equivalent torsional system shown, in Fig. P12-41(b). The necessary information is as
follows:

J of each rear wheel = 9.2 lb • in. • s^
J of flywheel = 12.3 lb • in.* s^
Transmission speed ratio (drive shaft to engine speed) = 1.0 to 3.0
Differential speed ratio (axle to drive shaft) = 1.0 to 3.5
Axle dimensions = 1^ in. diameter, 25 in. long (each)
Drive shaft dimensions = l | in. diameter, 74 in. long
Stiffness of crankshaft between cylinders, measured experimentally = 6.1 X 10^
lb *in./rad

Stiffness of crankshaft between cylinder 4 and flywheel = 4.5 X 10^ lb • in./rad

12-42 Assume that the J of each cylinder of Prob. 12-41 = 0.20 lb • in.* s^ and determine
the natural frequencies of the system.
12-43 Determine the equations of motion for the torsional system shown in Fig. P12-43, and
arrange them into the matrix iteration form. Solve for the principal modes of
oscillation.

50J

Gear ratio
= 5 tol
4J Figure P12-43.