Exercices

1

z
y
x
j
[Tij ] = 
T11 T12 0
T12 T22 0
0 0 T33 
θ
[Tij ] = 
1 0 0
0−1 1
0 1 −1
~
T
Ox1Ox2Ox3A(3,0,0) B(0,1,0)
C(0,0,1)
~
TN
~
TS
~
TSA B C
ρ= 7800 kg ·m−3
λ= 1.15 ×1011 P a µ = 0.77 ×1011 P a
U0= 1 µm f = 1 MHz
2

ϕ=Aexp [j(kx1cos (θ) + kx3sin (θ)−ωt)]
λ µ
T33
ρ0ρ(x, t)
Cαβ =
C11 C12 C13 000
C12 C11 C13 000
C13 C13 C33 000
000C44 0 0
0000C44 0
00000C66
ρ= 6,0×103kg.m−3
3

Cαβ =
C11 C12 C12 000
C12 C11 C12 000
C12 C12 C33 000
000C44 0 0
0000C44 0
00000C44
¯
1
Cαβ
ρ= 2733 kg.m−3
(x= 0) Txx =T0H(t)T0
H(t)
H(t) = 0t≤0
1t > 0
T0
λ+ 2µ= 1
x
t=d
cL
t=2d
cL
t=3d
cL
d cL
(ux(x, 0) = p(x)
∂ux
∂t (x, 0) = 0
p(x)
4

x ux(x, t)uF
x(k, t)k
x
ux(x, t)
t= 0
ux(x, 0) = p(x)
p(x) = 0 si x < 0
p(x) = Asin (πx)si 0< x < 1
p(x) = 0 si x > 1
A
x t = 0 t=1
2cLt=1 cL
x= 0 T11 =T0H(t)T0
H(t)
H(t) = 0si t 60
1si t > 0
ux(x, t) = −cLT0
λ+ 2µt−x cLHt−x cL
T0
λ+2µ= 1
x t =1
cLt=2 cLt=3 cL
ρ λ
µ
~u(x, t) = u(x, t)~ex
x= 0 −∞
T11(0, t) =
H(t)e−tH(t)
5