Air bearings are used to position and guide such axially-moving materials as high speed magnetic tapes, paper sheets, and webs. In each case, vibration of the moving medium couples with the air bearing’s dynamics, and techniques are developed here to reduce the computational effort that is required to predict the natural frequencies, damping ratios, and vibration modes of the prototypical traveling string and self-pressurized air bearing model. Automatic nodal point allocation reduces the number of nonlinear equations that arise in finding the equilibrium string displacement and air pressure, and in subsequent vibration analysis, the response is obtained in closed form by using the Green’s function for the traveling string. Global discretization of the air pressure alone then yields a matrix eigenvalue problem which is simpler than that obtained through previous methods which required discretization of both displacement and pressure. Overall, essentially a five-fold increase in computational speed is achieved, thus facilitating design and parameter studies. Changes in the natural frequencies, damping ratios, and coupled displacement-pressure mode shapes with respect to several design variables are discussed and compared with experiments.

1.
Daripa
P.
,
1991
, “
A New Theory for One-Dimensional Adaptive Grid Generation and Its Applications
,”
SIAM Journal of Numerical Analysis
, Vol.
28
, pp.
1635
1659
.
2.
Granzow, G. D., and Lebeck, A. O., 1984, “An Improved One-Dimensional Foil Bearing Solution,” Tribology and Mechanics of Magnetic Storage Systems, ASLE Special Publication, SP-16, pp. 54–58.
3.
Lacey
C. A.
, and
Talke
F. E.
,
1990
, “
A Tightly Coupled Numerical Foil Bearing Solution
,”
IEEE Transactions on Magnetics
, Vol.
26
, pp.
3039
3043
.
4.
Miller
K.
, and
Miller
R. N.
,
1981
, “
Moving Finite Elements I
,”
SIAM Journal of Numerical Analysis
, Vol.
18
, pp.
1019
1032
.
5.
Moes
H.
,
1991
, “
The Air Gap Between Tape and Drum in a Video Recorder
,”
Journal of Magnetism and Magnetic Materials
, Vol.
95
, pp.
1
13
.
6.
Ono
K.
,
Kodama
N.
, and
Michimura
S.
,
1991
, “
A New Numerical Analysis Method for Two-Dimensional Foil Bearing Problems Based on Inverse Analysis Concept
,”
JSME International Journal, Series III
, Vol.
34
, pp.
82
90
.
7.
Ono
K.
, and
Mizukawa
M.
,
1985
, “
Study on Spherical Foil Bearing; 3rd Report, Analysis for Large Bearing Penetration
,”
Bulletin of Japanese Society of Mechanical Engineers
, Vol.
28
, pp.
2097
2104
.
8.
Revilla
M. A.
,
1986
, “
Simple Time and Space Adaptation in One-Dimensional Evolutionary Partial Differential Equations
,”
International Journal for Numerical Methods in Engineering
, Vol.
23
, pp.
2263
2275
.
9.
Sanz-Serina
J. M.
, and
Christie
I.
,
1986
, “
A Simple Adaptive Technique for Nonlinear Wave Problems
,”
Journal of Computational Physics
, Vol.
67
, pp.
348
360
.
10.
Stahl
K. J.
,
White
J. W.
, and
Deckert
K. L.
,
1974
, “
Dynamic Response of Self-Acting Foil Bearings
,”
IBM Journal of Research and Development
, Vol.
18
, pp.
513
520
.
11.
Wickert
J. A.
, and
Mote
C. D.
,
1990
, “
Classical Vibration Analysis of Axially-Moving Continua
,”
ASME Journal of Applied Mechanics
, Vol.
57
, pp.
738
744
.
12.
Wickert
J. A.
, and
Mote
C. D.
,
1991
, “
Traveling Load Response of an Axially-Moving String
,”
Journal of Sound and Vibration
, Vol.
149
, pp.
267
284
.
13.
Wickert
J. A.
,
1993
, “
Free Linear Vibration of Self-Pressurized Foil Bearings
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
115
, pp.
145
151
.
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