An exact solution is provided to determine the effects of the free end boundary conditions and the slenderness ratios on the critical speed of two dimensional, axially moving materials. The axially moving beam theory and the mathematical, two-dimensional model with all edges simply supported are also considered for comparison.

1.
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
.
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