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Handbook of Turbomachinery Second Edition Revised - Ventech!

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Figure 6 The Laval–Jeffcott rotor.<br />

Laval–Jeffcott rotor model. The influence <strong>of</strong> both external and internal<br />

viscous damping on the translational motion is discussed later in this<br />

chapter. A discussion on the effects <strong>of</strong> rotatory (rotation perpendicular to<br />

the shaft centerline) inertia and gyroscopic moments <strong>of</strong> the disk are also<br />

included. The translational displacement components <strong>of</strong> the disk geometrical<br />

center, o, are denoted by ðu, vÞ relative to the ðx, yÞ-directions<br />

respectively.<br />

Undamped Response<br />

Relative to the ðx, y, zÞ reference, the equation <strong>of</strong> motion <strong>of</strong> the undamped<br />

two degree-<strong>of</strong>-freedom disk is<br />

m 0<br />

0 m<br />

€u<br />

€v þ kt 0<br />

0 kt<br />

Copyright © 2003 Marcel Dekker, Inc.<br />

u<br />

v ¼ meO2 cosðOtÞ<br />

sinðOtÞ<br />

ð4Þ

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