2 Excitation of the Waves with a Focused Source …
23
Fig. 2.1 Dependence of the square of the velocity of the surface wave from the wave number
We will look for the solution of this equation in the form: ψ = Be
i(ωt−kx) . We
get:
ω
2
= c
2
2 k
2
1 + L
2 k
2
, v
2
ph =
ω
2
k 2 = c
2
2
1 + L
2 k
2
,
v
2
ph
c
2
2
= (1 + α). (2.20)
From (2.20), it follows that the shear wave in a gradient-elastic medium has
dispersion, its phase velocity does not coincide with c 2 and exceeds it for any nonzero
value of the wave number.
Figure 2.2 presents two dependencies: the square of the surface wave velocity
C
2
R and the square of the shear wave phase velocity v
2
ph . The curves are presented in
Fig. 2.2 Dependence of the square of the velocity of the surface wave and the square of the phase
velocity of the shear wave from the wave number