Page 401 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

388 Classical Methods Chap. 12

Figure 12.4-1.
where harmonic motion is implied. This torque acts through shaft 1 and twists it by

6^ - 62 = I - 62
or

1 - T r

With 62 known, the inertia torque of the second disk is calculated as The
sum of the first two inertia torques acts through the shaft K 2, causing it to twist by

T<2

In this manner, the amplitude and torque at every disk can be calculated. The
resulting torque at the far end.

T’ex. = D
/-I
can then be plotted for the chosen cj. By repeating the calculation with other
values of w, the natural frequencies are found when = 0. The angular
displacements 6^ corresponding to the natural frequencies are the mode shapes.

Example 12.4-1
Determine the natural frequencies and mode shapes of the system shown in Fig.
12.4-2.

0.10x10^ /<2= 0.20x10^ Nm/rad

Figure 12.4-2.