Variational principle and bifurcations in stability analysis of panels
Julkaistu sarjassa
Reports of the Department of Mathematical Information Technology / University of Jyväskylä. Series B, Scientific computingPäivämäärä
2014In this paper, the stability of a simply supported axially moving elastic panel
is considered. A complex variable technique and bifurcation theory are applied.
As a result, variational equations and a variational principle are derived. Anal-
ysis 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 bifur-
cation 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 essen-
tial, because the presence of the fourth-order term in the model changes the
qualitative behaviour of the bifurcation points.
...
Julkaisija
Jyväskylän yliopistoISSN Hae Julkaisufoorumista
1456-436XAsiasanat
Metadata
Näytä kaikki kuvailutiedotSamankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Bifurcation method of stability analysis and some applications
Banichuk, Nikolay; Barsuk, Alexander; Neittaanmäki, Pekka; Jeronen, Juha; Tuovinen, Tero (Jyväskylän yliopisto, 2014)In this paper a new approach to the analysis of implicitly given function- als is developed in the frame of elastic stability theory. The approach gives an effective procedure to analyse stability behaviour, and to ... -
On modelling and stability of axially moving viscoelastic materials
Saksa, Tytti (University of Jyväskylä, 2013) -
The stress-strain state and stabilization of viscoelastoplastic, imperfect moving web continuum
Kurki, Matti (University of Jyväskylä, 2014) -
An analytical-numerical study of dynamic stability of an axially moving elastic web
Banichuk, Nikolay; Barsuk, Alexander; Neittaanmäki, Pekka; Jeronen, Juha; Tuovinen, Tero (Jyväskylän yliopisto, 2015)This paper is devoted to a dynamic stability analysis of an axially moving elastic web, modelled as a panel (a plate undergoing cylindrical deformation). The results are directly applicable also to the travelling beam. ... -
Mathematical models and stability analysis of induction motors under sudden changes of load
Solovyeva, Elena (University of Jyväskylä, 2013)
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.