res2nor
Purpose
Approximate transformation from complex residues to normal mode residue or proportionally damped normal mode forms.
Syntax
[Rres,po,Ridopt] = res2nor(Cres,po,Cidopt)
[wj,ga,cp,pb] = res2nor(Cres,po,Cidopt)
Description
The contributions of a pair of conjugate complex modes (complex conjugate poles 
and residues R) can be combined as follows
|
|
| [R] |
|
| s- |
|
+ |
|
|
| s- |
| - |
|
| |
|
|
|
=
2 |
(sRe (R)) + (  Re (R) -
(1-2)1/2Im (R)) |
|
| s2+2 s + 2 |
|
Under the assumption of proportional damping, the term
sRe(R) should be zero. res2nor, assuming that this is
approximately true, sets to zero the contribution in s and
outputs the normal mode residues Rres and the options Ridopt with Ridopt.Fit = 'Normal'.
When the four arguments of a normal mode model (see
nor )
are used as output arguments,
the function id_rm is used to extract the input pbs and output
cps shape matrices from the normal mode residues while the
frequencies wj and damping matrix ga are deduced from
the poles.
Warning
This function assumes that a proportionally damped model will allow
an accurate representation of the response. For more accurate results
use the function id_nor or identify using real residues (id_rc with
IDopt.Fit='Normal').
See also
id_rm, id_rc, id_nor, res2ss, res2xf
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