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

- all eigenfunctions form an orthogonal set of functions
npw : when
1 0 IPH ij--
S ot•tutdz=={
o0 1 11pH i=j
(3.39')
The last property is used in determining the natural frequencies
of vibrations and the form function for orders above the first
(i.e., ( e. wc2 ck and uk where k = 2, 3, 4 ... )
Integral equation (3.37) is usually solved by the method of
successive approximation (simple iteration). The advantage of this
method is the fact that with it it is possible to calculate a system
where all parameters are given numerically (tabular). As a result
of calculation, along with the frequencies, wave forms are obtained
which gives a concrete physical meaning to the solution of the
problem.
If a certain function is preset numerically, it is first
necessary to normalize this function.' This means that each value
of the function is divided by its norm (usually the norm tj the
peak value of the modulus of the function in the assigned range of
variation), i.e.,
'To compare two different functions of one class the concept of
the function norm exists. The function norm is the numerical value
of the important parameter or a set of parameters inherent in all
comparable functions, sometimes simply the "scale" of the function.
The norm of the function is designated 1hull or ul.
A function whose norm is equal to one is called normalized. In
vibration problems for the function norm we usually use the highest
value of the modulus of a function in a given range cc variation, which
can be dasignated ulmax.
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