Page 347 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

334 Introduction to the Finite Element Method Chap. 10

The new integral to be evaluated is
rl
mil^l / / / (p](pj drdx
'
which has been carried out and is equal to
0.600 0 -0.600 0.100/
0.100/2 0 -0.0166/2
n - mQ}l
0.600 -0.100/
0.0333/2
Assembling Matrices for Two-Element Beam

For the two-element beam, the assembled matrices are 6 x 6 . However, because
=0, the first two columns and rows are eliminated and we obtain a 4 X 4
matrix.

Mass
■ 156 22 54 -13 1 1 ■ 'c, = O'

22 4 13 - 3 1 = 0
ml 54 .3 r 156 -2 2 54 -13
420 1 156 22 1 < 02
-13 - 3 1 -2 2 4 1 13 -3
1 1
T ■ V 3
1 54 13 156 -2 2
1
1 .^3
-13 -3 -2 2 4_
312 0 54 -1 3 “ <V2\
ml 0 8 13 -3 62
7 \
420 54 13 156 -22 ^’3
. -13 -3 -22 4_
Stiffness
r 24 0 -12
t
'
il^2
0 8 - 6 ) 1 ^2
E l
- 12 - 6 12
P - t V3
6 2 - 6 A 1 1^3
Generalized force. From the first integral for Q, we have
0.8572 -0.0500 -0.4286 0.06429
-0.0500 0.0810 -0.01429 -0.009524
-0.4286 -0.01429 0.4286 -0.06429
0.06429 -0.009524 -0.06429 0.02381