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

I-I
We
shall designate
00 - z (0.36)
Then equation (3.35) can be written as
U = W2 K. (37)
As follows from the theory of integral equations, equatioq
(3.37) leads to a Fredholm linear homogeneous equation pf the second
kind with parameter X
(z)=)
K (zs) u (s) ds.
a (3.38)
which has a number of important properties allowing the use of these
equations for the solution of practical problems.
In equation (3.38) function y(s) i. unknown and must be
determined so that it is satisfied identicglly for all. values of z
in the range of a < z < b.
Function K(zs) is called the nucleus of this equation or Green's
function. The quantity X is called the parameter of the integral
equation, the eigenvalue or the eige-value of equation (3.38).
Equation (3.38) besides the trivial solution y(z) T 0, has
untrivial solutions in fully defined cases. The latter solutions
are called eigen or fundamental functions 6f equation (3.38).
c-rresponding to a given eigenvalue of X.
K(zs) is the nucleus of the integral equation Which determines
its fundamental properties and has a simple physical sense:
this iA
the function of the effect of an elastic system, i.e., tne amplitude
value of the deflection of a beam at an arbitrary point z under the
effect of a single source applied at point s.
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