This paper studies the friction induced vibrations that may develop in the neighborhood of steady sliding states of elastic orthotropic half-spaces compressed against a rigid plane moving tangentially with a prescribed speed. These vibrations may lead to flutter instability associated to a surfacelike oscillation. The system of dynamic differential equations and boundary conditions that governs the small plane oscillations of the half-space about the steady sliding state is established. The general form of the surface solutions to the plane strain case is given. The way how the coefficient of friction varies with changes in some of the system’s parameters is investigated. It is shown that for certain combinations of material data, low coefficients of friction are found for surface flutter instability (lower than in the isotropic case).

1.
Comninou
,
M.
, and
Dundurs
,
J.
, 1978, “
Elastic Interface Waves and Sliding Between Two Solids
,”
ASME J. Appl. Mech.
JAMCAV 0021-8936,
45
, pp. 325–330.
2.
Oden
,
J. T.
, and
Martins
,
J. A. C.
, 1985, “
Models and Computational Methods for Dynamic Friction Phenomena
,”
Comput. Methods Appl. Mech. Eng.
CMMECC 0045-7825,
52
, pp. 527–634.
3.
Pires
,
E. B.
, and
Trabucho
,
L.
, 1990, “
The Steady Sliding Problem With Nonlocal Friction
,”
Int. J. Eng. Sci.
IJESAN 0020-7225,
28
(
7
), pp. 631–641.
4.
Klarbring
,
A.
, and
Pang
,
J. -S.
, 1999, “
The Discrete Steady Sliding Problem
,”
Z. Angew. Math. Mech.
ZAMMAX 0044-2267,
79
(
2
), pp. 75–90.
5.
Martins
,
J. A. C.
,
Faria
,
L. O.
, and
Guimarães
,
J.
, 1992, “
Dynamic Surface Solutions in Linear Elasticity With Frictional Boundary Conditions
,”
Friction-Induced Vibration, Chatter, Squeal and Chaos
,
R. A.
Ibrahim
and
A.
Soom
, eds.,
ASME
,
New York
, Vol.
49
, pp. 33–39.
6.
Martins
,
J. A. C.
,
Guimarães
,
J.
, and
Faria
,
L. O.
, 1995, “
Dynamic Surface Solutions in Linear Elasticity and Viscoelasticity With Frictional Boundary Conditions
,”
ASME J. Vibr. Acoust.
JVACEK 0739-3717,
117
, pp. 445–451.
7.
Désoyer
,
T.
, and
Martins
,
J. A. C.
, 1998, “
Surface Instabilities in a Mooney–Rivlin Body With Frictional Boundary Conditions
,”
Int. J. Adhes. Adhes.
IJAADK 0143-7496,
18
, pp. 413–419.
8.
Adams
,
G. G.
, 1995, “
Self-Excited Oscillations of Two Elastic Half-Spaces Sliding With a Constant Coefficient of Friction
,”
ASME J. Appl. Mech.
JAMCAV 0021-8936,
62
, pp. 867–872.
9.
Adams
,
G. G.
, 1998, “
Steady-Sliding of Two Elastic Half-Spaces With Friction Reduction Due to Interface Stick-Slip
,”
ASME J. Appl. Mech.
JAMCAV 0021-8936,
65
, pp. 470–475.
10.
Adams
,
G. G.
, 2000, “
Radiation of Body Waves Induced by the Sliding of an Elastic Half-Space Against a Rigid Surface
,”
ASME J. Appl. Mech.
JAMCAV 0021-8936,
67
, pp. 1–5.
11.
Adams
,
G. G.
, 2000, “
Friction Reduction in the Sliding of an Elastic Half-Space Against a Rigid Surface Due to Incident Rectangular Dilatational Waves
,”
ASME J. Tribol.
JOTRE9 0742-4787,
122
, pp. 10–15.
12.
Adams
,
G. G.
, 1998, “
Dynamic Instabilities in the Sliding of Two Layered Elastic Half-Spaces
,”
ASME J. Tribol.
JOTRE9 0742-4787,
120
, pp. 289–295.
13.
Nosonovsky
,
M.
, and
Adams
,
G. G.
, 2000, “
Steady-State Frictional Sliding of Two Elastic Bodies With a Wavy Contact Interface
,”
ASME J. Tribol.
JOTRE9 0742-4787,
122
, pp. 490–495.
14.
Renardy
,
M.
, 1992, “
Ill-Posedness at the Boundary for Elastic Solids Sliding Under Coulomb Friction
,”
J. Elast.
JELSAY 0374-3535,
27
, pp. 281–287.
15.
Simões
,
F. M. F.
, and
Martins
,
J. A. C.
, 1998, “
Instability and Ill-Posedness in Some Friction Problems
,”
Int. J. Eng. Sci.
IJESAN 0020-7225,
36
, pp. 1265–1293.
16.
Ranjith
,
K.
, and
Rice
,
J. R.
, 2001, “
Slip Dynamics at an Interface Between Dissimilar Materials
,”
J. Mech. Phys. Solids
JMPSA8 0022-5096,
49
, pp. 341–361.
17.
Moirot
,
F.
,
Nguyen
,
Q. -S.
, and
Oueslati
,
A.
, 2003, “
An Example of Stick–Slip and Stick–Slip–Separation Waves
,”
Eur. J. Mech. A/Solids
EJASEV 0997-7538,
22
, pp. 107–118.
18.
Wang
,
Y. -S.
,
Yu
,
G. -L.
, and
Dai
,
H. -H.
, 2003, “
Transmission of Elastic Waves Through a Frictional Contact Interface Between Two Anisotropic Dissimilar Media
,”
Wave Motion
WAMOD9 0165-2125,
37
, pp. 137–156.
19.
Afferrante
,
L.
,
Ciavarella
,
M.
, and
Barber
,
J. R.
, 2006, “
Sliding Thermoelastodynamic Instability
,”
Proc. R. Soc. London, Ser. A
PRLAAZ 0950-1207,
462
, pp. 2161–2176.
20.
Afferrante
,
L.
, and
Ciavarella
,
M.
, 2007, “
Thermoelastic Dynamic Instability (TEDI) in Frictional Sliding of a Half-Space Against a Rigid Non-Conducting Wall
,”
ASME J. Appl. Mech.
JAMCAV 0021-8936,
74
, pp. 875–884.
21.
Vola
,
D.
,
Raous
,
M.
, and
Martins
,
J. A. C.
, 1999, “
Friction and Instability of Steady Sliding: Squeal of a Rubber/Glass Contact
,”
Int. J. Numer. Methods Eng.
IJNMBH 0029-5981,
46
(
10
), pp. 1699–1720.
22.
Fung
,
Y. C.
, 1965,
Foundations of Solid Mechanics
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
25.
Batoz
,
J. -L.
, and
Dhatt
,
G.
, 1990, Modélization des Structures par Éléments Finis. Vol. 1: solides élastiques, Hermes.
26.
Cook
,
R. D.
,
Malkus
,
D. S.
, and
Plesha
,
M. E.
, 1989,
Concepts and Applications of Finite Element Analysis
,
Wiley
,
New York
.
You do not currently have access to this content.