In linearly stable dynamical systems the non-normality of the corresponding linear operator is known to lead to transient growth of characteristic quantities, like, e.g., energy. For sliding friction systems it is shown in the present paper that this transient growth also applies to the sliding velocity and that under certain conditions this mechanism can lead to stick-slip limit-cycles in linearly stable system configurations.

1.
Farrell
,
B. F.
, 1988, “
Optimal Excitation of Perturbations in Viscous Shear Flow
,”
Phys. Fluids
0031-9171,
31
, pp.
2093
2102
.
2.
Waleffe
,
F.
, 1995, “
Transition in Shear Flows. Nonlinear Normality Versus Non-Normal Linearity
,”
Phys. Fluids
1070-6631
7
, pp.
3060
3066
.
3.
Grossmann
,
S.
, 1995, “
Wie Entsteht Eigentlich Turbulenz?
,”
Phys. Bl.
0031-9279,
51
, pp.
641
646
.
4.
Gebhardt
,
T.
, and
Grossmann
,
S.
, 1994, “
Chaos Transition Despite Linear Stability
,”
Phys. Rev. E
1063-651X,
50
, pp.
3705
3711
.
5.
Schmid
,
P. J.
, and
de Langre
,
E.
, 2003, “
Transient Growth Before Coupled-Mode Flutter
,”
ASME J. Appl. Mech.
0021-8936
70
, pp.
894
901
.
6.
Hoffmann
,
N.
, and
Gaul
,
L.
, 2004. “
Non-Conservative Beating in Sliding Friction Affected Systems: Transient Amplification of Vibrational Energy and a Technique to Determine Optimal Initial Conditions
,”
Mech. Syst. Signal Process.
0888-3270,
18
, pp.
611
623
.
7.
Popp
,
K.
,
Rudolph
,
M.
,
Krger
,
M.
, and
Lindner
,
M.
, 2002, “
Mechanisms to Generate and to Avoid Friction Induced Vibrations
,”
VDI-Ber.
0083-5560
1736
, pp.
1
15
.
8.
Hoffmann
,
N.
,
Fischer
,
M.
,
Allgaier
,
R.
, and
Gaul
,
L.
, 2002, “
A Minimal Model for Studying Properties of the Mode-Coupling Type Instability in Friction Induced Oscillations
,”
Mech. Res. Commun.
0093-6413
29
, pp.
197
205
.
9.
Hoffmann
,
N.
, and
Gaul
,
L.
, 2003, “
Effects of Damping on Mode-Coupling Instability in Friction Induced Oscillations
,”
Z. Angew. Math. Mech.
0044-2267
83
, pp.
524
534
.
10.
Hoffmann
,
N.
,
Bieser
,
S.
, and
Gaul
,
L.
, 2004, “
Harmonic Balance and Averaging Techniques for Stick-Slip Limit-Cycle Determination in Mode-Coupling Friction Self-Excited Systems
,”
Techn. Mech.
24
, pp.
185
197
.
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