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

Баничук, Н. В.; Jeronen, Juha; Neittaanmäki, Pekka; Tuovinen, Tero

doi:10.1016/j.jfluidstructs.2009.09.006

Cited by 36 publications

(22 citation statements)

References 27 publications

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“…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).…”

Section: Introductionmentioning

confidence: 77%

“…In the present paper, we extend into the dynamic case our earlier study, Banichuk et al (2010b), where the static instability of a travelling plate, undergoing small cylindrical deformation (see, e.g., Timoshenko and Woinowsky-Krieger 1959) and subjected to axial flow of ideal fluid, was studied. In the present study, we use an approach similar to Kornecki et al (1976), deriving the aerodynamic reaction analytically as a functional of the displacement, for the case where both the plate and the fluid are allowed to move axially, and flow occurs on both sides of the plate.…”

Section: Introductionmentioning

confidence: 99%

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

Баничук

Jeronen

Neittaanmäki

et al. 2011

Journal of Fluids and Structures

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The out-of-plane dynamic response of a moving plate, travelling between two rollers at a constant velocity, is studied, taking into account the mutual interaction between the vibrating plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the plate (assumed cylindrical), is described by an integrodifferential equation that includes a local inertia term, Coriolis and centrifugal forces, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, the bending resistance, and external perturbation forces. In the two-dimensional model thus set up, the aerodynamic reaction is found analytically as a functional of the cylindrical displacement, using the techniques of complex analysis. The resulting integro-differential problem is discretized in space with the Fourier-Galerkin method, and integrated in time with the diagonalization method. Examples are computed with physical parameters corresponding to air and some paper materials. The effects of the surrounding fluid on the critical velocity and first natural frequency are investigated, for stationary air, for an air mass moving with the plate, and for some arbitrary axial fluid velocities. The obtained results are applicable for both an ideal membrane and a plate with nonzero bending rigidity.

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Section: Introductionmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

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

Баничук

Jeronen

Neittaanmäki

et al. 2011

Journal of Fluids and Structures

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“…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. Chen et al [2008] modeled accelerating viscoelastic strings with asymptotic approach and analyzed the steady-state response with the method.…”

Section: Introductionmentioning

confidence: 99%

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

Chang

Wang

et al. 2018

Int. J. Appl. Mechanics

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In the manufacturing of low-strength composites sheets, the symmetry-breaking bifurcation phenomenon may happen when the sheets are transported by rolls, which can lead to vibration and crack in the sheets. However, the mechanism and the conditions for this phenomenon has not been studied so far. In this paper, we propose a theoretical model to study the formation mechanism of the bifurcation phenomenon in a driven-idle-driven rolls system, and the critical length of the thin-sheets between rolls is obtained, above which the bifurcation will happen. Results show that the bifurcation occurs because the relationship between the lengths of the sheet between rolls and the tension caused by gravity in sheets is not monotonic, and the critical length is about 2.5 times the distance between the rolls. We also carry out experiments to verify the validity of the proposed model. This study is of great importance for the design of the multi-roll system to transport the low strength sheet materials, such as paper and composite sheets.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Research on the Transportation of Low-Strength Composites Sheets

Chang

Wang

et al. 2017

Applied Sciences

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Abstract:The novel non-combustible sandwich panel is extremely fragile in manufacturing and cannot be tensioned between rolls. Previous studies on the roll-to-roll system, which mainly focused on the high-tension situations and little described the low-strength materials, are insufficient. To explore the transportation of low-strength materials, we study the tension distribution of continuous moving flexible one-dimensional materials on a steady-state track. First, we propose a numerical method to calculate the steady-state track of low-strength sheet between rolls considering the gravity, as well as size and position of rolls. Then we obtain the optimum sag at different size and position of rolls. We find out that there is a lower limit of the sheet's strength-density ratio (the Minimum Specific Strength) for a specific set of size and position of rolls. Finally, we establish a method to calculate the lower limit approximately for engineering use. Our method can be generalized in manufacturing other low-strength flexible thin-sheet materials as well.

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

Cited by 36 publications

References 27 publications

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

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

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

Research on the Transportation of Low-Strength Composites Sheets

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