On the limit velocity and buckling phenomena of axially moving orthotropic membranes and plates
Banichuk, N., Jeronen, J., Kurki, M., Neittaanmäki, P., Saksa, T., & Tuovinen, T. (2011). On the limit velocity and buckling phenomena of axially moving orthotropic membranes and plates. International Journal of Solids and Structures, 48 (13), 2015-2025. doi:10.1016/j.ijsolstr.2011.03.010
Published inInternational Journal of Solids and Structures
© Elsevier. This is an author's final draft version of an article whose final and definitive version has been published by Elsevier.
In this paper, we consider the static stability problems of axially moving orthotropic membranes and plates. The study is motivated by paper production processes, as paper has a fiber structure which can be described as orthotropic on the macroscopic level. The moving web is modeled as an axially moving orthotropic plate. The original dynamic plate problem is reduced to a two-dimensional spectral problem for static stability analysis, and solved using analytical techniques. As a result, the minimal eigenvalue and the corresponding buckling mode are found. It is observed that the buckling mode has a shape localized in the regions close to the free boundaries. The localization effect is demonstrated with the help of numerical examples. It is seen that the in-plane shear modulus affects the strength of this phenomenon. The behavior of the solution is investigated analytically. It is shown that the eigenvalues of the cross-sectional spectral problem are nonnegative. The analytical approach allows for a fast solver, which can then be used for applications such as statistical uncertainty and sensitivity analysis, real-time parameter space exploration, and finding optimal values for design parameters. ...
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On static instability and estimates for critical velocities of axially moving orthotropic plates under inhomogeneous tension Saksa, Tytti; Jeronen, Juha (Jyväskylän yliopisto, 2012)In this study, models for axially moving orthotropic plates are investigated analytically. Linearised Kirchhoff plate theory is used, and the energy forms of steady-state models are considered. With the help of the energy ...
Banichuk, Nikolay; Jeronen, Juha; Neittaanmäki, Pekka; Saksa, Tytti; Tuovinen, Tero (Elsevier, 2013)Problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity, are studied using analytical approaches. Transverse vibrations of the web are described by a partial differential ...
Banichuk, Nikolay; Jeronen, Juha; Neittaanmäki, Pekka; Saksa, Tytti; Tuovinen, Tero (Springer, 2014)
Banichuk, Nikolay; Jeronen, Juha; Ivanova, Svetlana; Tuovinen, Tero (University of Jyväskylä, 2014)
Analysis of stability of axially moving orthotropic membranes and plates with a linear non-homogeneous tension profile Tuovinen, Tero (University of Jyväskylä, 2011)