On the instability of an axially moving elastic plate

Abstract

a b s t r a c tProblems of stability of an axially moving elastic band travelling at constant velocity between two supports and experiencing small transverse vibrations are considered in a 2D formulation. The model of a thin elastic plate subjected to bending and tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of an analytical approach. In the frame of a general dynamic analysis, it is shown that the onset of instability takes place in the form of divergence (buckling). Then the static forms of instability are investigated, and critical regimes are studied as functions of geometric and mechanical problem parameters. It is shown that in the limit of a narrow strip, the 2D formulation reduces to the classical 1D model. In the limit of a wide band, there is a small but finite discrepancy between the results given by the 1D model and the full 2D formulation, where the discrepancy depends on the Poisson ratio of the material. Finally, the results are illustrated via numerical examples, and it is observed that the transverse displacement becomes localised in the vicinity of free boundaries.

Dynamic behaviour of an axially moving plate undergoing small cylindrical deformation submerged in axially flowing ideal fluid

“…First of all, the cylindrical deformation assumption is a reasonable approximation only for narrow strips, as was noted in our previous study, Banichuk et al (2010b). This is explained by the form of the problem: even for the static case in a vacuum, it can be shown (for details, see our earlier study, Banichuk et al 2010a) that for a pinned-free plate, the deformation becomes localised in the vicinity of the free boundaries, and that the buckling shape is that of eigenfunctions of free vibrations of a stationary rectangular plate (given, e.g., in Gorman 1982). Secondly, the viscoelasticity, which introduces damping into the system, is ignored.…”

A Study on the Symmetry-Breaking Bifurcation Phenomenon in Transportation of Low-Strength Composites Sheets by Rolls

“…Mote [1990, 1991] Chen et al [2009] reviewed the research on transverse vibrations and their control of axially moving strings. Frondelius et al [2006] and Banichuk et al [2010a] studied the interaction of axially moving strings and the surrounding fluid. Laukkanen [2002] and Banichuk et al [2010b] modeled axially moving sheet as 2D plates with FEM and analytic methods, respectively, and analyzed the vibration of the sheet with proposed model.…”

Research on the Transportation of Low-Strength Composites Sheets

“…Those approximations lead to the consequence that the track of the traveling materials is an approximately straight line. For example, the studies on the transverse vibrations of axially moving materials [2][3][4][5][6][7][8][9][10][11][12][13][14] and studies on the transverse vibration control technique of axially moving materials [15][16][17][18][19][20] all neglected the effect of gravity on the sheet and treated the traveling materials as tensioned. This means that the sag of the moving sheet is small compared to the distance between two rolls.…”