Wave reflection and transmission in composite beams containing ...

ARTICLE IN PRESS
W.-C. Yuan et al. / Journal of Sound and Vibration 313 (2008) 676–695 687
Magnitude
180
ω/ω c
3
0.6
R
0
12
R 0
R
2
22
11
0.3
R
-45
-45
21 1
(2) (1)
ω c ω c ω c
1.5
180 7
ω c
(2)
ω c
(1)
ω c
ω/ω c
1.2
135
6
135
90
5
90
0.9
4
45
45
0
-90 0
-90
0 1 2 3 4
0 1 2 3 4
Phase (deg)
Fig. 5. Reflection coefficients (R jk , for j, k ¼ 1,2) (h 1 /h ¼ 0.4) under closed delamination condition (solid line: magnitude; dotted line:
phase). Wave reflection from (a) first flexural mode and (b) second flexural mode.
Magnitude
Phase (deg)
2.0
(2) (1)
ω c ω c ω c
135
25
(2) (1)
ω c ω c ω c
180
Magnitude
1.5
1.0
0.5
(1)
(1) T 21
T 11
(1)
T 31
90
45
0
-45
Phase (deg)
Magnitude
20
15
10
5
(1)
T 22
(1)
T 12
(1)
T 32
135
90
45
0
-45
-90
Phase (deg)
0 -90
0 1 2 3 4
ω/ω c
0
-135
0 1 2 3 4
ω/ω c
Fig. 6. Magnitudes and phases of transmission coefficients ðT ð1Þ
jk ; for j ¼ 1,2,3, k ¼ 1,2) in upper sub-beam (h 1/h ¼ 0.4) under open
delamination condition (solid line: magnitude; dotted line: phase). Wave transmission from (a) first flexural mode and (b) second flexural
mode.
2.0
(2) (1)
ω c ω c ω c
135
25
(2) (1)
ω c ω c ω c
180
Magnitude
1.5
1.0
0.5
(2)
T 11
(2)
T 21
(2)
T 31
90
45
0
-45
Phase (deg)
Magnitude
20
15
10
5
(2)
T 22
(2)
T 12
(2)
T 32
135
90
45
0
-45
-90
Phase (deg)
0
-90
0 1 2 3 4
ω/ω c
0
-135
0 1 2 3 4
ω/ω c
Fig. 7. Magnitudes and phases of transmission coefficients (T ð2Þ
jk , for j ¼ 1,2,3, k ¼ 1,2) in lower sub-beam (h 1/h ¼ 0.4) under open
delamination condition (solid line: magnitude; dotted line: phase). Wave transmission from (a) first flexural mode and (b) second flexural
mode.