Interaction of an axially moving band and surrounding fluid by boundary layer theory

Static instability analysis for travelling membranes and plates interacting with axially moving ideal fluid

“…A recent study by Frondelius et al (2006) suggests that due to the boundary layer, the divergence velocities in viscous fluid may be significantly higher than those predicted by the ideal fluid model. Thus, the present results should be primarily seen as academical basic research concerning axial flow phenomena and axially moving materials.…”

“…According to the same study, the boundary layer is negligible even in the case with longitudinal transportation, and thus potential flow predictions should apply there also. However, in a recent paper, Frondelius et al (2006) show that the boundary layer does have an effect, especially near the critical velocity of the vibrating medium. While the eigenfrequency predictions agree with those from potential flow theory, the divergence velocities are found to be significantly higher.…”

“…To solve the external aerodynamic problem, and to find the reaction of the surrounding medium, the finite element method has been used (Niemi and Pramila 1986). Added-mass approaches are also common, usually in combination with a finite element solution (Pramila 1986, Pramila 1987, and for a modi-fied version with boundary layer theory, Frondelius et al 2006). …”

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.…”