The exact expression describing the contact force between an axially moving flexible strip and a one-sided constraint is derived using the Green’s function formulation. Discontinuity of the initial velocity at a boundary of the strip due to a disturbance, causes discontinuity in the contact force history at any constraint that is not modeled by a single spring element. The discontinuities in the contact force occur at the instants when those propagating wavefronts in the strip with nonvanishing slope interact with the constraint. A model of a magnetic tape-recording head system is analyzed. Tape-head contact loss is predicted, depending on the amplitude and frequency of a disturbance, the head location, and the preload of the tape against the head.

1.
Hoskins, R. F., 1979, Generalised Functions, Ellis Horwood Limited, Chichester, U.K.
2.
Linz, P., 1985, Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia, PA.
3.
Perkins
N. C.
,
1990
, “
Linear Dynamics of a Translating String on an Elastic Foundation
,”
ASME Journal of Vibration and Acoustics
, Vol.
112
, pp.
2
7
.
4.
Perkins
N. C.
, and
Mote
C. D.
,
1986
, “
Comments on Curve Veering in Eigenvalue Problems
,”
Journal of Sound and Vibration
, Vol.
106
, No.
3
, pp.
451
463
.
5.
Sack
R. A.
,
1954
, “
Transverse Oscillations in Travelling Strings
,”
British Journal of Applied Physics
, Vol.
5
, pp.
224
226
.
6.
Schajer
G. S.
,
1984
, “
The Vibration of a Rotating Circular String Subject to a Fixed Elastic Restraint
,”
Journal of Sound and Vibration
, Vol.
92
, No.
1
, pp.
11
19
.
7.
Stakgold, I., 1979, Green’s Functions and Boundary Value Problems, John Wiley and Sons, New York.
8.
Wickert
J. A.
, and
Mote
C. D.
,
1990
, “
Classical Vibration Analysis of Axially Moving Continua
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
57
, No.
3
, pp.
738
744
.
9.
Wickert
J. A.
, and
Mote
C. D.
,
1991
, “
Traveling Load Response of an Axially-Moving String
,”
Journal of Sound and Vibration
, Vol.
149
, No.
2
, pp.
267
284
.
10.
Yang
B.
,
1992
, “
Eigenvalue Inclusion Principles for Distributed Gyroscopic Systems
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
59
, pp.
650
656
.
11.
Zhu
W. D.
, and
Mote
C. D.
,
1994
, “
Free and Forced Response of an Axially Moving String Transporting a Damped Linear Oscillator
,”
Journal of Sound and Vibration
, Vol.
177
, No.
5
, pp.
591
610
.
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