4 - Memorial University of Newfoundland DAI

A.l Diagonalization of a Consistent Mass Ma-
trix Using Cook's Method
Cark [48] mmmenda a pmsedure which nppliea la clcments whoso trasa.
lational DOF are mutually parallel (e.g., beam and plnle elemetnta). 'The
scheme is summarized as:
1. Compute only the diagonnlized coefficients of tile wnsistcnt XUMS stn-
trix.
2. ComputeX, the lotni mass of lhe element.
3. Computeanumbcra by adding tlle diagonal mcnicientsmij RSROC~~~LII
with translation, but not rotation.
4. Conlpute the diagonal eoelficientsm:, by mtrilipiyir~g them Ihy tile ndio
-
M; this pmservea the translationni mass of the clemcst.
Thus, iI the following n x n consistent mass matrix is ~vnilsbio:
7",, m12 m,3 ... m,"
m21 m22 mw . . . mt.,
. . . . . . .
m.1 m.2 mnJ .. . mnn
This malrix is diagonalie 0 , .I, ~g Cook's suggestions) ~ n:
m;, 0 0 ... 0
0 m;, 0 ... 0
. . . ... .
0 0 0 ... m;