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Friction-Induced Vibrations and Self-Organization
book

Friction-Induced Vibrations and Self-Organization

by Michael Nosonovsky, Vahid Mortazavi
August 2013
Intermediate to advanced content levelIntermediate to advanced
333 pages
11h 16m
English
CRC Press
Content preview from Friction-Induced Vibrations and Self-Organization
211From Frictional Instabilities to Friction-Induced Self-Organization
ψττ
′′
τ=
′′
=
XXXfXdX(,)(,; ,0)( )
X 0
1
(8.16)
Comparing Equation (8.16) with Equation (8.15), one can construct the
Green’s function by replacing τ by ττ′:
γτ
′′
τ=
ππ
=
−πτ−
τ
XX em
Xm
X(,;,02 sin( )sin
()
m
m
1
()()
2
(8.17)
where X and τ′
are integration parameters. Then, the solution of the non-
homogeneous problem is given in terms of Green’s function (Mortazavi et
al. 2012):
∫∫
ψτ=
ψτ+
τγτ−
τ
′′
τ=
τ
=
∈τ
XXdG
XX
dX(,)(,) exp(,,)
X
G
00
1
(8.18)
Substituting Equation (8.17) into Equation (8.18) yields the solution of
Equation (8.14):
ψτπ
′′
+
π−
π−
π<
<
()
=
−πτ
=
=
−∫τ
XemX mX fX ...
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Publisher Resources

ISBN: 9781466504011