The pipeline parametric
resonance under elastic deformation
S.V.Kashirin, G.A.Shcheglov
Sometimes pipelines are the most important
elements of the construction. One of the possible ways of mass reduction of
such elements is connected with the reduction of pipe wall thickness. For
pipelines with thin walls it is important to consider elastic compliance of
cross-section when analyzing pipeline dynamics. There is also an actual problem
of parametric vibrations investigation of such systems.
The results of analysis of pipelines contained
liquid with small pressure pulsation are presented. There pulsations of a
liquid stream and variable axial force were considered as external excitation.
The purpose of the present research is to estimate influence of pulsations of
internal pressure in the pipeline and the deformation of pipeline cross-section
as one of the excitation factor, which can cause parametrical vibrations.
In the present research the dead-end pipeline
with motionless liquid is considered. This case is sufficiently important
because it simulates pipelines blocked with gate.
It is considered in this model,
that the average diameter of the pipe changes under influence of
pressure pulsations. The pipeline is considered to be thin shell with big
lengthening. So according to momentless shells theory
(an edge effect is neglected) we can write the diameter increment. Change of
diameter of the pipe leads to change of cross-section moment of inertia and
linear mass of the liquid.
Parametric vibrations investigation
is carried out using asymptotic method in the first approximation.
The analysis of equation shows, that
to a first approximation only the principal parametric resonance is available.
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