The thermoelastic coupling vibration characteristics of the axially moving beam with frictional contact are investigated. The piecewise differential equation of motion for the axially moving beam in the thermoelastic coupling case and the continuous conditions at the contact point are established. The eigenequation is derived by the differential quadrature method, and the first order dimensionless complex frequencies of the simply supported axially moving beam under the coupled thermoelastic case are calculated. The effects of the dimensionless thermoelastic coupling factor, the dimensionless moving speed, the spring stiffness, the friction coefficient, and the normal pressure on the thermoelastic coupling vibration characteristics of the axially moving beam with frictional contact are discussed.

1.
Simpson
,
A.
, 1973, “
Transverse Modes and Frequencies of Beams Translating Between Fixed and Supported
,”
J. Mech. Eng. Sci.
0022-2542,
15
(
3
), pp.
159
164
.
2.
Wickert
,
J. A.
, and
Mote
,
C. D.
, 1990, “
Classical Vibration Analysis of Axially Moving Continua
,”
ASME J. Appl. Mech.
0021-8936,
57
, pp.
738
744
.
3.
Wickert
,
J. A.
, and
Mote
,
C. D.
, 1991, “
Response and Discretization Methods for Axially Moving Materials
,”
ASME J. Appl. Mech.
0021-8936,
44
, pp.
S279
S284
.
4.
Chakraborty
,
G.
, and
Mallik
,
A. K.
, 2000, “
Wave Propagation in and Vibration of a Traveling Beam With and Without Non-Linear Effects
,”
J. Sound Vib.
0022-460X,
236
(
2
), pp.
277
290
.
5.
Kong
,
L.
, and
Parker
,
G.
, 2004, “
Approximate Eigensolutions of Axially Moving Beams With Small Flexural Stiffness
,”
J. Sound Vib.
0022-460X,
276
(
1–2
), pp.
459
469
.
6.
Yang
,
X. D.
, and
Chen
,
L. Q.
2007, “
Determination of the Natural Frequencies of Axially Moving Beams by the Method of Multiple Scales
,”
J. Shanghai Univ.
,
11
(
3
), pp.
251
254
.
7.
Avsec
,
J.
, and
Oblak
,
M.
, 2007, “
Thermal Vibrational Analysis for Simply Supported Beam and Clamped Beam
,”
J. Sound Vib.
0022-460X,
308
(
3–5
), pp.
514
525
.
8.
Manoach
,
E.
, and
Ribeiro
,
P.
, 2004, “
Coupled, Thermoelastic, Large Amplitude Vibrations of Timoshenko Beams
,”
Int. J. Mech. Sci.
0020-7403,
46
(
11
), pp.
1589
1606
.
9.
Chang
,
W. P.
, and
Wan
,
S. M.
, 1986, “
Thermomechanically Coupled Nonlinear Vibration of Plates
,”
Int. J. Non-Linear Mech.
0020-7462,
21
(
5
), pp.
375
389
.
10.
Eslami
,
M. R.
,
Shakeri
,
M.
, and
Sedaghati
,
R.
, 1994, “
Coupled Thermoelasticity of Axially Symmetric Cylindrical Shell
,”
J. Therm. Stresses
0149-5739,
17
(
1
), pp.
115
135
.
11.
Copper
,
C. D.
, and
Pilkey
,
W. D.
, 2002, “
Thermoelasticity Solutions for Straight Beams
,”
ASME J. Appl. Mech.
0021-8936,
69
(
5
), pp.
224
229
.
12.
Guo
,
F. L.
, and
Rogerson
,
G. A.
, 2003, “
Thermoelastic Coupling Effect on a Micro-Machined Beam Resonator
,”
Mech. Res. Commun.
0093-6413,
30
(
6
), pp.
513
518
.
13.
Sun
,
Y. X.
,
Fang
,
D. N.
, and
Ai
,
K. S.
, 2006, “
Thermoelastic Damping in Micro-Beam Resonators
,”
Int. J. Solids Struct.
0020-7683,
43
(
10
), pp.
3213
3229
.
14.
Guo
,
X. X.
,
Wang
,
Z. M.
,
Wang
,
Y.
, and
Zhou
,
Y. F.
, 2009, “
Analysis of the Coupled Thermoelastic Vibration for Axially Moving Beam
,”
J. Sound Vib.
0022-460X,
325
(
3
), pp.
597
608
.
15.
Kang
,
B.
, and
Tan
,
C. A.
, 2004, “
Parametric Instability of a Leipholz Beam Due to Distributed Frictional Axial Load
,”
Int. J. Mech. Sci.
0020-7403,
46
(
6
), pp.
807
825
.
16.
Cheng
,
S. P.
, and
Perkins
,
N. C.
, 1991, “
The Vibration and Stability of a Friction-Guided, Translating String
,”
J. Sound Vib.
0022-460X,
144
(
2
), pp.
281
292
.
17.
Chen
,
J. S.
, 1997, “
Natural Frequencies and Stability of an Axially-Traveling String in Contact With a Stationary Load System
,”
ASME J. Vibr. Acoust.
0739-3717,
119
, pp.
152
157
.
18.
Adams
,
G. G.
, 1996, “
Self-Excited Oscillations in Sliding With a Constant Friction Coefficient—A Simple Model
,”
ASME J. Tribol.
0742-4787,
118
, pp.
819
823
.
19.
Mottershead
,
J. E.
, and
Chan
,
S. N.
, 1995, “
Flutter Instability of Circular Discs With Frictional Follower Loads
,”
ASME J. Vibr. Acoust.
0739-3717,
117
, pp.
161
163
.
20.
Daniel
,
H.
,
Gottfried
,
S. K.
, and
Peter
,
H.
, 2007, “
Friction Induced Vibrations in Moving Continua and Their Application to Brake Squeal
,”
ASME J. Appl. Mech.
0021-8936,
74
, pp.
542
549
.
21.
Gottfried
,
S. K.
,
Kirillov
,
O. N.
, and
Peter
,
H.
, 2008, “
Modeling and Stability Analysis of an Axially Moving Beam With Frictional Contact
,”
ASME J. Appl. Mech.
0021-8936,
75
, p.
031001
.
You do not currently have access to this content.