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

I.
Each of the harmonics of the angular frequ ency. of forced
vibriations c cd is a multipl6 of-'ngular v~elocity w of the rotor;
the. order of harmoniic k determines thicIýultiplicity:
Ii
a
I
a
Wkk~kT~iC,(3.52)
where k is the'harmonic number; k = 1, 2, 3, ..
is the number of revolutions of týLe rotor per second.
Forced ýribrations by themselves will be dangerous if the value
of tche exciting force is high, able 1 to cause *ignif'icant amplitudes
vsibnfiatos ampis ~tudes of-vbatosanda vleadngty of blae breakown.
of vibrations. I However,lin practice, a the so-called resonance modes
will- be dangelrous.
As we knowfthe dondition ofresonance is the equality of
forced frequencies W, Wk t o the frequeficies of natural vibrations
a W.~c. a(3-53)
In this 6ase, even small forces are capable if causing
I'I a I
h .7n a turbine a large nkdmber of different harmonics of excitation
can ocur.e However
not all thetse harmonics will be dangerous from
.'be point of view of resonance. To vstlablish th', degree of danger'
for any harmonic a frequency (resonac~nce) df ýgrain M(P.. 3.30) has
* been plotted for each turbine stage. The dia~x'ain is a graph of the
lependence * of th Ie frequencie's of free I [detek:Aneci oy eq-t~tiori (3.418)]
and Ikcrced [see equation 1 63-52)] vibrations of a blade on the angular
velocity or the nmnber ox' revolutions o per second.
In A
iew.. of the difficulty of obtaining curves P =
pflottinga frequency diagram k
P(t) when
and a preliminary evalusation of the
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