6.10 Transfer Matrix Method
211
Fig. 6.14 Mode shapes of Example 6.7
and
{Z }
R
2 =
1
k
0
Substituting the value of the second frequency, p
2
2 =
2k
m
in the above relations,
we get
{Z }
L
1 =
1
2k
1
, {Z }
R
1 =
1
2k
− 1
, {Z }
L
2 =
−
1
2k
− 1
and
{Z }
R
2 =
−
1
2k
0
The mode shapes are plotted in Fig. 6.14.
The results of the normal modes can be checked by the orthogonality property.
1
i = 1
m 1 φ
(1)
i φ
(2)
1
= 2m × 1 × 1 + m × 1 × (− 2) = 0
6.11 Myklestad Method
Like Holzer method, calculations are performed progressively from one station to
another. In this section, Myklestad method has been presented for the vibrating beam.