6.13 Matrix Deflation Procedure
227
The first mode shape is given by
{φ
(1)
} =
⎧
⎨
⎩
1.000
0.759
0.336
⎫
⎬
⎭
To determine an appropriate starting iteration vector, we are required to deflate
the unit full iteration vector {φ
(1)
}
{φ} =
⎧
⎨
⎩
1.000
1.000
1.000
⎫
⎬
⎭
− α 1
⎧
⎨
⎩
1.000
0.759
0.336
⎫
⎬
⎭
where α 1 given by Eq. (6.95) is
α 1 =
1.000 0.759 0.336
m
⎡
⎣
1.0 0 0
0 1.0 0
0 0 1.0
⎤
⎦
⎧
⎨
⎩
1.000
1.000
1.000
⎫
⎬
⎭
1.000 0.759 0.336
m
⎡
⎣
1.0 0 0
0 1.0 0
0 0 1.0
⎤
⎦
⎧
⎨
⎩
1.000
0.759
0.336
⎫
⎬
⎭
or α 1 = 1.24.
Therefore,
{φ} =
⎧
⎨
⎩
1.000
1.000
1.000
⎫
⎬
⎭
− 1.24
⎧
⎨
⎩
1.000
0.759
0.336
⎫
⎬
⎭
=
⎧
⎨
⎩
− 0.240
0.059
0.583
⎫
⎬
⎭
We can normalise {φ} such that
{φ} =
⎧
⎨
⎩
− 4.067
1.000
9.881
⎫
⎬
⎭
The iteration process can now be started with this trial vector
m
6k
⎡
⎣
8 5 2
5 5 2
2 2 2
⎤
⎦
⎧
⎨
⎩
− 4.067
1.000
9.881
⎫
⎬
⎭
=
4.427m
6k
⎧
⎨
⎩
− 1.756
1.000
3.078
⎫
⎬
⎭