Design and Stress Analysis of Extraterrestrial ... - The Black Vault

If the number of disks in the rotor is more than one, the
frequency equation is made considerably more complicated. Thus, for
a two-disk system the determinant (3.115, will have the form
C 2 1 c2--(hi -- JUs) C23 cC24
f 3 l f32 ('ý 34
C41 C 42 C 43 C44 (JVA2 JnS) Il
(3.136)
and the frequency equation will be of the 8th power relative to X
2
(or of the 4th power relative to X
For a three-disk system the frequency equation will be of the
12th power relative to Xetc. These equations become-difficult to
solve by ordinary methods.
It should be noted that high speed computers, however, can
solve this problem. There are other methods also which, if we use
some approximation, enable us to determine the critical angular
velocities of complex systems. Among these methods is the solution
to integral equations of free vibrations using the method of
successive approximations.
The integral equation for free flexural vibrations in a rotating
rotor on two supports, having an arbitrary law of variation for the
cross-sectional area of the shaft along the length and a loadcarrying
raw of disks located arbitrarily along the length (Fig. 3.78)
has the form
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