res2nor

Contents Functions

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 λ and residues R) can be combined as follows

[R]

s−λ

[R]

s−λ

= 2

(sRe (R)) + (ζω Re (R) − ω

√

1−ζ²

Im (R))

s²+2ζω s + ω²

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').