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

satisfies the bounaary conditions of the r oblem (this function is
already normalized).
Fig. 3.27. Integration of
the f(x) function by the
trapezoid method.
The analysis will use formula (3.25).
performed according to the trapezoid method.'
Integration will be
Integration in lines (8)
and (15) begins from the blade tip
since according to the boundary conditions when = 1, the shearing
force is equal to zero. Integrat:!on in.lines (9) and (16) is also
performed from the blade tip (wh.2n i = 1 the bending moment is zero).
In lines (11), (18) and (12), (19) we integrate from the beginning
of reading (since when z - 0 the angle of pitch and the deflection
of the blade are equal to zero).
Both the zero and the subsequent approximations of function
uare drawn on the graph (Fig. 3.26).
The angular velocity of natural blade vibrations is determined
from formula (3.45), taking into account the remote factor:
'As we know, the formula of trapezoids has the following form
(if the number of points of division is equal to n) (see Fig. 3.27)
f (.) dx - Ax (fo +- fI + 2f2 +... + 2f -, + f J), where Ax=- .
2 n
The greater n the more accurate the formula.
278