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

Differentiating this equation, we find the expression for
shearing force:
d2M =
dZ'
(c)
After we differentiate equation (c)
for linear load from the internal elastic forces:
once more, we obtain an expression
d2M" __.-L = q =(EI~')".
dz2
dz
(d)
Let us make the external linear load equal to the linear load
from -internal -forces--[equations, (a' -) -and (d-)]; -then the general
differential equation for an oscillating blade will be written in
the form
(Ehi')" +eFI--=0. (3.-19),
To solve differential equation -(3.19) ].t us use Fourier t s
method - the separation of variables z and t. We shall introduce
designations:
Trjz, t)=u(z), g(W)=ug,
where u(z) is the function of deflection, depending only on the z
coordinate;
g(t) is the function of deflection depending only or time t.
If we differentiate equation (e) four times with respect to
z and two times with respect to t and substitute these derivatives
into equation (3.19), we obtain
,,,, ' -- , •
(3.20)
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