
150 Friction-Induced Vibration and Self-Organization
Equations (6.104) and (6.105) are solved for p/g with the use of Equations
(6.106) and (6.107):
=
−
+ε
π
ε+ −ε −ε +
−α
π
ε+ −ε −ε
−
π
+
−α
+
π
+
−α
+
p
g
a
a
IIaI aI T IIaIaI
T
KJ J
T
Ka
a
1
2
2
()
12
2
1
2
12
2
1
2
12
2
1
22
12
22
2
2
301
22
1
2
2
10
(6.106)
=−
+ε
ε+ −ε
−+
p
g
a
a
IIaIaI
JK aK J
ri22
01
22
1
2
2
(6.107)
where
∫
∫
=
−+
+
=
=
−+
+
=
−α −+α
−
−α −+α
I
ss s
as
ds m
I
ss s
as
ds m
(1 )(1)
(1 )
0,1, 2,3
(1 )(1)
1
0,1, 2
m
m
m
m
1
222
1
1
1
22
1
(6.108)
When combined together, Equations (6.106) and (6.107) constitute a quadratic
equation for ε that has two roots, ε
1
and ε
2
, such that their product is equal
to –1/a
2
. These two roots correspond to ...