FEM analysis of a travelling web

Laukkanen, J.

doi:10.1016/s0045-7949(02)00214-6

Cited by 14 publications

(7 citation statements)

References 16 publications

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“…To make sure the existence of nontrivial solutions of (16), the determinant of the coefficient matrix should be set to zero. The first four complex natural frequencies, namely, ω 11 , ω 12 , ω 21 , ω 22 , can be calculated for different values of parameters of axially moving speed and pretension. Each natural complex frequency can be denoted as, ω = Re(ω) ± Im(ω), where the real part Re(ω) stands for the actual free vibration natural frequency and imaginary part Im(ω) is related to the variation of the amplitude caused by the input or output of the energy.…”

Section: Complex Natural Frequency Analysismentioning

confidence: 99%

“…Starting from velocity γ = 0, the imaginary parts of all orders keep zero while the real parts decrease (Case 1). At γ = 13.4660, which is called critical speed, the real part of (1, 1) mode natural frequency vanishes and the imaginary part begins to be [20][21][22].…”

Section: Complex Natural Frequency Analysismentioning

confidence: 99%

“…Wang [20] used a mixed finite element formulation to study the natural frequencies of a moving MindlinReissner plate. Laukkanen [21] introduced shear correction techniques to enhance the efficiency of a finite element method in investigation of a moving thin plate. Hatami et al used the finite strip method to investigate an axially moving plate of viscoelastic material [22].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical analysis of axially moving plate by finite difference method

et al. 2011

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The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion of the plate is derived by Newton's second law. The finite difference method in spatial field is applied to the differential equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion, and then the periodic motion becomes chaotic motion by period-doubling bifurcation.

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Section: Complex Natural Frequency Analysismentioning

confidence: 99%

Section: Complex Natural Frequency Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical analysis of axially moving plate by finite difference method

et al. 2011

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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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FEM analysis of a travelling web

Cited by 14 publications

References 16 publications

Dynamical analysis of axially moving plate by finite difference method

Dynamical analysis of axially moving plate by finite difference method

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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