Analytical approach for the problems of dynamics and stability of a moving web
Banichuk, N., Jeronen, J., Ivanova, S., & Tuovinen, T. (2015). Analytical approach for the problems of dynamics and stability of a moving web. Rakenteiden mekaniikka, 48(3), 136-163. http://rmseura.tkk.fi/rmlehti/2015/nro3/RakMek_48_3_2015_1.pdf
Published in
Rakenteiden mekaniikkaDate
2015Copyright
© The Authors 2015. This is an open access article under CC BY-SA 4.0 license.
Problems of dynamics and stability of a moving web, modelled as an elastic rod or
string, and axially travelling between rollers (supports) at a constant velocity, are studied using
analytical approaches. Transverse, longitudinal and torsional vibrations of the moving web are
described by a hyperbolic second-order partial differential equation, corresponding to the string
and rod models. It is shown that in the framework of a quasi-static eigenvalue analysis, for these
models, the critical point cannot be unstable. The critical velocities of one-dimensional webs,
and the arising non-trivial solution of free vibrations, are studied analytically. The dynamical
analysis is then extended into the case with damping. The critical points of both static and
dynamic types are found analytically. It is shown in the paper that if external friction is present,
then for mode numbers sufficiently high, dynamic critical points may exist. Graphical examples
of eigenvalue spectra are given for both the undamped and damped systems. In the examples,
it is seen that external friction leads to stabilization, whereas internal friction in the travelling
material will destabilize the system in a dynamic mode at the static critical point. The theory
and results summarize and extend theoretical knowledge of the class of models studied, and can
be used in various applications of moving materials, such as paper making processes.
...
![showless](/themes/JYX2//images/showless.png)
![showmore](/themes/JYX2//images/showmore.png)
Publisher
Rakenteiden Mekaniikan Seura ryISSN Search the Publication Forum
0783-6104Keywords
Original source
http://rmseura.tkk.fi/rmlehti/2015/nro3/RakMek_48_3_2015_1.pdfPublication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/25407515
Metadata
Show full item recordCollections
License
Except where otherwise noted, this item's license is described as © The Authors 2015. This is an open access article under CC BY-SA 4.0 license.
Related items
Showing items with similar title or keywords.
-
Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large
Leonov, G.A.; Kuznetsov, Nikolay; Yuldashev, Marat; Yuldashev, Renat (Elsevier BV; European Association for Signal Processing, 2015)The analysis of the stability and numerical simulation of Costas loop circuits for highfrequency signals is a challenging task. The problem lies in the fact that it is necessary to simultaneously observe very fast time ... -
A realist approach to thematic analysis : making sense of qualitative data through experiential, inferential and dispositional themes
Wiltshire, Gareth; Ronkainen, Noora (Routledge, Taylor & Francis, 2021)Thematic analysis (TA) is the most widely used method for analysing qualitative data. Recent debates, highlighting the binary distinctions between reflexive TA grounded within the qualitative paradigm and codebook TA with ... -
The spanning tree based approach for solving the shortest path problem in social graphs
Eremeev, Andrei (2016)This thesis is devoted to the shortest path problem in social graphs. Social graphs represent individuals and social relationships between them. As for social networking sites, their users are represented as vertices of ... -
Patterns of action transitions in online collaborative problem solving : A network analysis approach
Li, Shupin; Pöysä-Tarhonen, Johanna; Häkkinen, Päivi (Springer Science and Business Media LLC, 2022)In today’s digital society, computer-supported collaborative learning (CSCL) and collaborative problem solving (CPS) have received increasing attention. CPS studies have often emphasized outcomes such as skill levels of ... -
A thermoelastic instability problem for axially moving plates
Banichuk, Nikolay; Ivanova, Svetlana; Jeronen, Juha; Makeev, Evgeni; Neittaanmäki, Pekka; Tuovinen, Tero (University of Jyväskylä, 2016)Problems of stability and deformation of a moving web, traveling between a system of rollers at a constant velocity are considered. The plate is subjected to a combined thermomechanical loading, including pure mechanical ...