University of Jyväskylä

Dissertation: Analysis of stability of axially moving orthotropic membranes and plates with linear non-homogeneous tension profile (Tuovinen)

Start date: Dec 17, 2011 12:00 PM

End date: Dec 17, 2011 03:00 PM

Location: Mattilanniemi, Agora, auditorium 3

Tero TuovinenM.Sc. Tero Tuovinen defends his doctoral dissertation titled “Analysis of stability of axially moving orthotropic membranes and plates with linear non-homogeneous tension profile”. Opponent Professor (emeritus) Heikki Koivo (Aalto University) and TkT Kari Juppi (Metso paper) and custos Professor Pekka Neittaanmäki (University of Jyväskylä).


The topic of this thesis relates to the classical problem of the stability of moving materials.  We have studied problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity using analytical and numerical approaches. The stability of the plate is investigated with the help of studies of small out-of-plane vibrations. The influence of linearly distributed in-plane tension on the characteristics of the web vibrations
is studied as well.

Our analysis is based on models of axially moving orthotropic membranes and plates. The static forms of instability are investigated using numerical methods, and an estimate for the divergence speed of a membrane is expressed with the help of in-plane strain and material parameters. The original dynamic plate problem is reduced to a two-dimensional spectral problem and solved using analytical techniques. As a result, the minimal eigenvalue and the corresponding buckling mode are found. This study has been extended to consider a linear non-homogeneous tension profiles as well.The materials based on published articles have been extended and re-written and new results have been introduced for the thesis.

The conclusion of this thesis is that the effect that originates from the orthotropic material is moderate, while the tension profile plays an important role in the shaping of the buckling mode. It can be concluded that inhomogeneities in the applied tension may significantly decrease the critical web velocities, and even small inhomogeneities in the tension may have a large effect on the divergence forms. In particular, the effect of the localization of transverse displacements in the vicinity of free boundaries is illustrated. The obtained results match the experimental knowledge; they can be used for an effective estimation of the critical velocity as a function of mechanical and geometric problem parameters.

Further information:

Tero Tuovinen, tel. 040 531 0791,

The dissertation is published in the series Jyväskylä Studies in Computing no 146, Jyväskylä: University of Jyväskylä, 2011, 104 p., ISSN 1456-5390; 146, ISBN 978-951-39-4577-0, ISBN 978-951-39-4578-7 (PDF). Inquiries: University Library, Publishing Unit, tel. 040 805 3825,
The dissertation is available online at:

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