Exact free vibration analysis of axially moving viscoelastic plates

Hatami, S.; Ronagh, Hamid Reza; Azhari, Mojtaba

doi:10.1016/j.compstruc.2008.02.002

Cited by 87 publications

(28 citation statements)

References 22 publications

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“…In order to better understand energy dissipation mechanism of such materials, some viscoelastic constitutive relations like the Kelvin-Voigt form have been used to describe mechanical behaviors of the materials, which is widely applied in axially moving continuums such as strings [18,19], beams [20,21], belts [22,23], and plates [24,25]. In addition, some structures made of more complex viscoelastic materials are explored.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

Li¹,

Tang²

2017

Mathematical Problems in Engineering

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The nonlinear parametric vibration of an axially moving string made by rubber-like materials is studied in the paper. The fractional viscoelastic model is used to describe the damping of the string. Then, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton's second law, the Euler beam theory, and the Lagrangian strain. Taking into consideration the fractional calculus law of Riemann-Liouville form, the principal parametric resonance is analytically investigated via applying the direct multiscale method. Numerical results are presented to show the influences of the fractional order, the stiffness constant, the viscosity coefficient, and the axial-speed fluctuation amplitude on steady-state responses. It is noticeable that the amplitudes and existing intervals of steady-state responses predicted by Kirchhoff 's fractional material model are much larger than those predicted by Mote's fractional material model.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

Li¹,

Tang²

2017

Mathematical Problems in Engineering

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“…In this approach, the displacements are considered as functions which satisfy at least the various geometric boundary conditions. Based on Navier's procedure, the solution of the displacement variables can be expressed in the following forms [15]: (13) A. …”

Section: Analytical Solutionmentioning

confidence: 99%

“…To solve the differential equations governing the problem, they have used both the Galerkin method and differential quadrature method. In the case of free vibration analysis of axially moving viscoelastic plates, Hatami et al [15] and Marynowski [16] have studied. However, each of them has used different models for their work.…”

Section: Introductionmentioning

confidence: 99%

Vibration Characteristics of Axially Moving Titanium- Polymer Nanocomposite Faced Sandwich Plate Under Initial Tension

Arani

Haghparast²,

Zarei³

2017

International Journal of Engineering &Amp; Applied Sciences

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“…The loss of stability of axially moving plates was investigated by Banichuk et al 3) in a two-dimensional formulation, taking into account their bending resistance and in-plane tension. Hatami et al 4) presented an exact finite strip model for the free vibration analysis of axially moving viscoelastic plates. Tan and 5) developed an active vibration control scheme based on wave cancellation for an axially moving string with general boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Research on Vibration Control Method of Steel Strip for a Continuous Hot-dip Galvanizing Line

Yan

Guo

et al. 2012

ISIJ Int.

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Nonlinear vibration of axially moving steel strip with tension near the air knife box during continuous hot-dip galvanizing process is investigated. A model of strip vibration for cooling section is established. Governing equations of the model are derived through the Hamilton's principle. Effect of speed, tension, molten zinc, oscillation of touch rolls and nonlinear wind load on strip vibration is considered. The reasonability of boundary conditions of the model is confirmed by comparison of results from theoretical method and numerical simulation. Averaging method is employed in solving the equations and obtaining displacement response. The relation between amplitude near the air knife and production parameters is studied and further solutions of vibration control is presented. The research reveals that speed of strip has noticeable effect on amplitude near the air knife. It will be more difficult to reduce vibration with the increase of speed. Larger tension is in favor of keeping away from peaks of amplitude by using speed adjustment. A scheme of vibration control based upon averaging method can meet the requirement of production. A vibration suppression proposal by improving support stiffness of touch rolls is suggested.KEY WORDS: averaging method; wind load of air knife; strip tension; strip speed; touch roll.

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Exact free vibration analysis of axially moving viscoelastic plates

Cited by 87 publications

References 22 publications

Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

Vibration Characteristics of Axially Moving Titanium- Polymer Nanocomposite Faced Sandwich Plate Under Initial Tension

Research on Vibration Control Method of Steel Strip for a Continuous Hot-dip Galvanizing Line

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