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8.44
Derive a consistentmass matrix for the system of Figure 8.9.
Compare the
natural frequencies of this system with those calculated with the lumpedmass
matrix computed in Section 8.5.
Solution:
Using the vibration toolbox
M
=
ρΑλ
.6857
0
0
.7238
The natural frequencies are then
ϖ
1
= .8311
1
l
E
r
and
w
1
=1.479
1
l
E
r
These are higher than those predicted with the inconsistent mass matrix
8.45
Consider the two beam system of Figure P8.45.
Use VTB8_1 to create a two
element, rod/beam element model and compute the first three natural frequencies.
Use
A
= 0.0004 m
2
,
I
= 1.33
×
10
8
m
4
, and the properties of aluminum.
Assume
that nodes 1 and 3 are clamped.
Solution:
%scipt file for problem 8.45
node=[0 0;1 .5;2 1;1
1.5;0 2];
ncon=[1 2 69e10 .004 1.33e8 0 2700;
2 3 69e10 .004 1.33e8 0 2700;
3 4 69e10 .004 1.33e8 0 2700;
4 5 69e10 .004 1.33e8 0 2700];
zero=[1 1;
1 2;
1 3;
5 1;
5 2;
5 3];
conm=[];
force=[];
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This note was uploaded on 11/28/2010 for the course ME 4440 taught by Professor Hill during the Winter '09 term at Detroit Mercy.
 Winter '09
 Hill

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