Variational approach for analysis of harmonic vibration and stabiligy of moving panels
Banichuk, N., Barsuk, A., Tuovinen, T., & Jeronen, J. (2014). Variational approach for analysis of harmonic vibration and stabiligy of moving panels. Rakenteiden mekaniikka, 47(4), 148-162. http://rmseura.tkk.fi/rmlehti/2014/nro4/RakMek_47_4_2014_2.pdf
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Rakenteiden mekaniikkaDate
2014Copyright
© the Authors © Rakenteiden Mekaniikan Seura ry.
In this paper, the stability of a simply supported axially moving elastic panel (plate
undergoing cylindrical deformation) is considered. A complex variable technique and bifurcation
theory are applied. As a result, variational equations and a variational principle are derived.
Analysis of the variational principle allows the study of qualitative properties of the bifurcation
points. Asymptotic behaviour in a small neighbourhood around an arbitrary bifurcation point
is analyzed and presented.
It is shown analytically that the eigenvalue curves in the (ω, V0) plane cross both the ω and
V0 axes perpendicularly. It is also shown that near each bifurcation point, the dependence ω(V0)
for each mode approximately follows the shape of a square root near the origin.
The obtained results complement existing numerical studies on the stability of axially moving
materials, especially those with finite bending rigidity. From a rigorous mathematical viewpoint,
the presence of bending rigidity is essential, because the presence of the fourth-order term in the
model changes the qualitative behaviour of the bifurcation points. The results are applicable to
both axially moving panels and axially moving beams.
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Rakenteiden Mekaniikan Seura ryISSN Search the Publication Forum
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https://converis.jyu.fi/converis/portal/detail/Publication/24475647
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