
145Friction-Induced Instabilities and Vibrations
Here the ratio of longitudinal (C
L
) and shear (C
S
) wave speeds are
β=
=
−
−
C
C
v
v
2(
12
k
L
S
k
k
(6.78)
in which k = 1 for the upper body and k = 2 for the lower body.
The deformed state of the bodies was considered as the superposition of
uniform stresses (caused by the dimensionless applied pressure
=ppG
and dimensionless tangential traction μp and the dimensionless residual
stresses
σ=
ij
k
ij
k
k
() ()
. The boundary conditions at innity (|y| = ∞) state
that stresses and strains should be bounded. On the contact surface (y = 0);
here, are two kinds of boundary conditions: non-mixed and mixed ...