Divergence and Parametric Instability of Belts by using Bolotin Method

Abstract

Belt is a traveling continuous
system.Such a system can subjected to a
static divergence and parametric
instability. This depend on whether the
system parameters are constant or
varying with the time ,respectively .In
this paper ,instability problem is solved
analytically .Bolotin method is used to
evaluate the boundaries which separate
the stable and instable regions.The
present solution is checked with another
solution available in the literature where
the Variation principle is used .The
results showed a good agreement where
the maximum error do not exceed 5%.
The effect of belt tension and
transmitting speed on stability and
natural frequency are studied .The
results show that increasing belt tension
can improve both buckling and
parametric instability. Whilst, increasing
the speed or its mean value is limited to
critical values to avoid buckling or
parametric instability, respectively.