a análise de placas laminadas compostas inteligentes
a análise de placas laminadas compostas inteligentes
a análise de placas laminadas compostas inteligentes
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7.5 Solução <strong>de</strong> Navier 144<br />
∞<br />
∞<br />
m=1 n=1<br />
+<br />
∞<br />
<br />
+<br />
L11α 2 m + L66β 2 <br />
<br />
n Umn + L12 + L66 αmβnVmn + F11α 2 m + F66β 2 <br />
n Xmn<br />
F12 + F66<br />
+ 3Dc55<br />
+ αm<br />
m=1 n=1<br />
<br />
<br />
αmβnYmn +<br />
Xmn + αmWmn<br />
npiez <br />
k=1<br />
3e (k)<br />
15<br />
m=1 n=1<br />
1<br />
hk<br />
<br />
<br />
H11α 2 m + H66β 2 <br />
n Xmn + H12 + H66 αmβnYmn<br />
+ 9F c55Xmn + αm<br />
npiez <br />
k=1<br />
4 zk 12 − zkz3 k−1<br />
3 + z4 <br />
k−1<br />
Φ<br />
4<br />
(k−1)<br />
mn<br />
e (k)<br />
31<br />
1<br />
4hk<br />
(z 4 k − z 4 k−1)Φ (k−1)<br />
mn<br />
<br />
cos αmx sin βny e iωt<br />
∞ ∞<br />
<br />
npiez<br />
<br />
<br />
<br />
3Dc45 Ymn + βnWmn + 9F c45Ymn + βn e<br />
k=1<br />
(k) 1<br />
36<br />
4hk<br />
npiez <br />
+ βn 3e<br />
k=1<br />
(k) 1<br />
4 zk 25<br />
hk 12 − zkz3 k−1<br />
3 + z4 <br />
k−1<br />
Φ<br />
4<br />
(k−1)<br />
<br />
mn sin αmx cos βny e iωt<br />
= −ω 2<br />
∞ ∞<br />
<br />
<br />
cos αmx sin βny e iωt<br />
∞<br />
L12 + L66<br />
<br />
m=1 n=1<br />
<br />
+ F66α 2 m + F22β 2 n<br />
+<br />
+ 3Dc44<br />
∞<br />
+ βn<br />
m=1 n=1<br />
<br />
ρ3Umn + ρ4Xmn + ρ6Xmn<br />
αmβnUmn +<br />
<br />
Ymn +<br />
Ymn + βnWmn<br />
npiez <br />
k=1<br />
3e (k)<br />
24<br />
∞<br />
<br />
3Dc45<br />
+ αm<br />
= −ω 2<br />
npiez <br />
k=1<br />
∞<br />
1<br />
hk<br />
<br />
(z 4 k − z 4 k−1)Φ (k−1)<br />
mn<br />
<br />
L66α 2 m + L22β 2 <br />
n Vmn + F12 + F66 αmβnXmn<br />
H12 + H66<br />
<br />
+ 9F c44Ymn + βn<br />
αmβnXmn +<br />
npiez <br />
k=1<br />
4 zk 12 − zkz3 k−1<br />
3 + z4 <br />
k−1<br />
Φ<br />
4<br />
(k−1)<br />
mn<br />
<br />
e (k)<br />
32<br />
<br />
H66α 2 m + H22β 2 <br />
n Ymn<br />
1<br />
4hk<br />
(z 4 k − z 4 k−1)Φ (k−1)<br />
mn<br />
<br />
sin αmx cos βny e iωt<br />
npiez <br />
1<br />
(7.95)<br />
Xmn + αmWmn + 9F c45Xmn + αm e<br />
k=1<br />
(k)<br />
36 (z<br />
4hk<br />
4 k − z 4 k−1)Φ (k−1)<br />
mn<br />
3e (k) 1<br />
4 zk 14<br />
hk 12 − zkz3 k−1<br />
3 + z4 <br />
k−1<br />
Φ<br />
4<br />
(k−1)<br />
<br />
mn cos αmx sin βny e iωt<br />
∞<br />
<br />
m=1 n=1<br />
ρ3Vmn + ρ4Ymn + ρ6Ymn<br />
<br />
sin αmx cos βny e iωt<br />
(7.96)