74
4 Multi-Degree of Freedom (MDOF) Systems
Fig. 4.2 Discrete
approximation of a
continuous system
Fig. 4.3 Trials 1, 2, and 3
ω 1 = 3.156
E I
m h 4 , ω 2 = 16.258
E I
m h 4 , 1 =
0.3111
0.9504
and
2 =
0.8366
−0.5477
.
We approximate ω 1 from Eq. 4.13 with u = [1 1] T (Trial 1), u = [a 2 a] T , a > 0,
(Trial 2), and u = [a h 2 /4 a h 2 ] T , a > 0, (Trial 3), see Fig. 4.3. The approximations
of ω 1 for these trials are
ω 1 8.5524
E I
m h 4 (error: + 171%),
ω 1 4.2763
E I
m h 4 , (error: + 35%),
ω 1 3.4913
E I
m h 4 (error: + 10.6%).
4 Multi-Degree of Freedom (MDOF) Systems
Fig. 4.2 Discrete
approximation of a
continuous system
Fig. 4.3 Trials 1, 2, and 3
ω 1 = 3.156
E I
m h 4 , ω 2 = 16.258
E I
m h 4 , 1 =
0.3111
0.9504
and
2 =
0.8366
−0.5477
.
We approximate ω 1 from Eq. 4.13 with u = [1 1] T (Trial 1), u = [a 2 a] T , a > 0,
(Trial 2), and u = [a h 2 /4 a h 2 ] T , a > 0, (Trial 3), see Fig. 4.3. The approximations
of ω 1 for these trials are
ω 1 8.5524
E I
m h 4 (error: + 171%),
ω 1 4.2763
E I
m h 4 , (error: + 35%),
ω 1 3.4913
E I
m h 4 (error: + 10.6%).