An analytical-numerical study of dynamic stability of an axially moving elastic web
Published inReports of the Department of Mathematical Information Technology / University of Jyväskylä. Series B, Scientific computing
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. In accordance with the dynamic approach of stability analysis, the problem of harmonic vi- brations is investigated via the study of the dependences of the system’s nat- ural frequencies on the problem parameters. Analytical implicit expressions for the solution curves, with respect to problem parameters, are derived for ranges of the parameter space where the natural frequencies are real-valued, corresponding to stable vibrations. Both axially tensioned and non-tensioned travelling panels are considered. The special cases of the non-tensioned trav- elling panel, and the tensioned stationary (non-travelling) panel are also dis- cussed, and special-case solutions given. Numerical evaluation of the obtained general analytical results is discussed. Numerical examples are given for panels subjected to two different tension levels, and for the non-tensioned panel. The results allow the development of very efﬁcient, lightweight solvers for deter- mining the natural frequencies of travelling panels and beams. The results can also be used to help locate the bifurcation points of the solution curves, corre- sponding to points where mechanical stability is lost. ...
Alternative titleAnalytical-numerical study of dynamic stability of an axially moving elastic web
MetadataShow full item record
Showing items with similar title or keywords.
Saksa, Tytti (University of Jyväskylä, 2013)
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 ...
Banichuk, Nikolay; Barsuk, Alexander; Tuovinen, Tero; Jeronen, Juha (Jyväskylän yliopisto, 2014)In 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 ...
Analytical-numerical analysis of closed-form dynamic model of Sayano-Shushenskaya hydropower plant : stability, oscillations, and accident Kuznetsov, N.V.; Yuldashev, M.V.; Yuldashev, R.V. (Elsevier, 2021)This work is devoted to the analysis of a mathematical model of hydropower unit, consisting of synchronous generator, hydraulic turbine, and speed governor. It is motivated by the accident happened on the Sayano-Shushenskaya ...
Kurki, Matti (University of Jyväskylä, 2014)