8 Interaction of Harmonic Waves of Different Types …
113
Fig. 8.1 Model of interaction between soil and plate: a is the ingoing wave; b is the cylindrical
ingoing wave
There is two kind of influence being observed—flat wave and cylindrical one. The
normal vector of the plane is lying inside the plane Oxy, due to this, components of
disturbance-deformation state of barrier and soil are independent from axis Y, and
due to this only normal disturbance is being accounted. The main aim is definition
of normal movement in half space «2» after passing through barrier (Fig. 8.1).
The main target is definition of sum of vector field of acceleration a, inducted
by passed and emitted waves in half space «2» as frequency function ω and spatial
coordinates x and z dependent from plates parameters. Components a x and a z , and
module a of vector field of accelerations are defined by this formulas:
a x = −ω
2 u
(2)
, a z = −ω
2 w
(2)
.
(8.1)
a =
a 2
x + a 2
z ,
(8.2)
where u and w—movement along axis Ox and Oz.
The mathematical formulation of the problem includes the task of the incident
wave, the equations of motion of the soil and the plate, boundary conditions for the
plate and the ground, conditions at infinity, as well as the conditions of contact of the
soil with an obstacle, where we neglect the adhesion of the plate with the ground.
113
Fig. 8.1 Model of interaction between soil and plate: a is the ingoing wave; b is the cylindrical
ingoing wave
There is two kind of influence being observed—flat wave and cylindrical one. The
normal vector of the plane is lying inside the plane Oxy, due to this, components of
disturbance-deformation state of barrier and soil are independent from axis Y, and
due to this only normal disturbance is being accounted. The main aim is definition
of normal movement in half space «2» after passing through barrier (Fig. 8.1).
The main target is definition of sum of vector field of acceleration a, inducted
by passed and emitted waves in half space «2» as frequency function ω and spatial
coordinates x and z dependent from plates parameters. Components a x and a z , and
module a of vector field of accelerations are defined by this formulas:
a x = −ω
2 u
(2)
, a z = −ω
2 w
(2)
.
(8.1)
a =
a 2
x + a 2
z ,
(8.2)
where u and w—movement along axis Ox and Oz.
The mathematical formulation of the problem includes the task of the incident
wave, the equations of motion of the soil and the plate, boundary conditions for the
plate and the ground, conditions at infinity, as well as the conditions of contact of the
soil with an obstacle, where we neglect the adhesion of the plate with the ground.