118
L. Igumnov et al.
In the equation system (8.24), the further notation is used: w c , w a —deflections;
q
1 —transverse shear stress in the filling along the x-axis; u
(k)
1 —tangential displacement along the x-axis, respectively, in the k-th bearing layer. B i D—tangent and
bending stiffness of the tangent plate. w
(k) —the deflection of k bearing layer
u
a
1 = u
(1)
0 − u
(2)
0 ;
w c = w
(1)
0 + w
(2)
0 , w a = w
(1)
0 − w
(2)
0 .
Conditions on the simply supported contour of the plate
w
(1)
0
x=0,l
= w
(2)
0
x=0,l
= u
(1)
,x
x=0,l
= u
(2)
,x
x=0,l
= q
1
,x
x=0,l
= 0,
w
(1)
0 ,xx
x=0,l 1
= w
(2)
0 ,xx
x=0,l 1
= 0.
(8.25)
8.6 Conditions on the Contact Surface
The pressure amplitude of the wave coming from the medium «1» is equal to the sum
of the normal stress in the medium and stress, arising as a result of the wave action.
In the second medium, the pressure amplitude is the same as the normal stress.
The plane harmonic wave
p 1 =
σ
(1)
33 + σ 33∗
z=0
, p 2 = −σ
(2)
33
z=0
.
(8.26)
w
(1)
+ w ∗
z=0
= w
(1)
0 , w
(2)
z=0
= w
(2)
0 ,
σ
(1)
13
z=0
= σ
(2)
13
z=0
= 0, σ
(1)
12
z=0
= σ
(2)
12
z=0
= 0, σ
(1)
23
z=0
= σ
(2)
23
z=0
= 0.
(8.27)
The cylindrical harmonic wave
p 1n = (σ 33∗n + σ 33n )| z=0 , p 2n = −σ
(2)
33n
z=0
,
σ
(1)
13n
z=0
= σ 13∗ | z=0 ;
(8.28)
w
(1)
n + w ∗n
z=0
= w
(1)
0n
z=0
,
w
(2)
n
z=0
= w
(2)
0n
z=0
, u
(1)
0n
z=0
= u ∗ | z=0 .
(8.29)