Modelling the dynamical behaviour of a paper web. Part II

Kulachenko, Artem; Gradin, Per; Koivurova, H.

doi:10.1016/j.compstruc.2006.09.007

Cited by 48 publications

(21 citation statements)

References 18 publications

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“…It was observed that the presence of fluid, in all cases, significantly reduces the first natural frequency when compared to the vacuum case. This matches known results; see, e.g., Kulachenko et al (2007b) and Pramila (1986).…”

Section: Resultssupporting

confidence: 92%

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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: Resultssupporting

confidence: 92%

“…It can be seen that the presence of fluid decreases the first natural frequency, as expected (see Pramila, 1986, andKulachenko et al, 2007b).…”

Section: Numerical Resultssupporting

confidence: 84%

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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“…This is not a major problem, as the introduction of damping is not expected to change the critical velocity, although it does modify the postdivergence behaviour (Mote and Ulsoy, 1982). Finally, the interaction between the travelling web and the surrounding air, which is not accounted for in the present study, is known to influence the critical velocity (Pramila, 1986;Frondelius et al, 2006) and the dynamical response (Kulachenko et al, 2007), possibly also affecting the buckling shape.…”

Section: Introductionmentioning

confidence: 90%

On the instability of an axially moving elastic plate

Баничук

Jeronen

Neittaanmäki

et al. 2010

International Journal of Solids and Structures

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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.

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“…Shin [12] derived equations of motion for the moving membrane with no-slip boundary conditions at rollers by using the extended Hamilton principle, and investigated the dynamic characteristics of the out-of-plane vibration for an axially moving membrane. A depth study about the nonlinear dynamic behavior of the membrane has been developed [13][14]. Marynowski [15] modeled the axially moving viscoelastic web material by using two-dimensional rheological theory.…”

Section: Journal Of Low Frequency Noise Vibration and Active Controlmentioning

confidence: 99%

Transverse Vibration Characteristics and Stability of a Moving Membrane with Elastic Supports

Lei

et al. 2014

Journal of Low Frequency Noise, Vibration and Active Control

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The transverse vibration characteristics and stability of a moving membrane with several intermediate elastic supports are investigated considering the translating speed. The motion equations of the vibration system are derived according to the membrane vibration theory and the D'Alembert principle. The constraint of the middle printing roller to the membrane is used as the intermediate support which is replaced by the constraint force. And the vibration characteristic equation is established by using Laplace transformation method and the numerical calculation method. Finally, the relationships between the natural frequency of the moving membrane and the translating speed, tension, supporting position and rigidity modulus are analyzed respectively, and the critical speed when the membrane is in a stable state is obtained. The conclusions provide a theoretical basis and effective approaches for improving the work stability of the printing press.

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Modelling the dynamical behaviour of a paper web. Part II

Cited by 48 publications

References 18 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

On the instability of an axially moving elastic plate

Transverse Vibration Characteristics and Stability of a Moving Membrane with Elastic Supports

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