Dynamical analysis of axially moving plate by finite difference method

Yang, Xiao‐Dong; Zhang, Wei; Chen, Liqun; Yao, Minghui

doi:10.1007/s11071-011-0042-2

Cited by 79 publications

(25 citation statements)

References 30 publications

(46 reference statements)

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“…Many researchers applied directly extended Hamilton's principle to study the nonlinear vibration of axially moving beams and plates with simple geometric conditions such as Ghayesh and Farokhi [2015], Tang et al [2008], Seddighi and Eipakchi [2016], Ding and Zu [2013], Ali and Elham [2017]. Based on the extended Hamilton principle, Zhang et al obtained many remarkable results for the nonliner vibration of the axially moving beam or plate [Cao and Zhang, 2006, Chen et al, 2007, Chen et al, 2010, Yao et al, 2012, Yang et al, 2012, Yang and Zhang, 2014 But, these works did not point out clearly what description has been used. Koivurova and Salonen [1999] reviewed and clarified the kinematic aspects of nonlinear governing equations of axially moving structures.…”

Section: Introductionmentioning

confidence: 99%

Kinematic Aspects in Modeling Large-Amplitude Vibration of Axially Moving Beams

Wang

Ding

Chen

2019

Int. J. Appl. Mechanics

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This paper clarified kinematic aspects of motion of axially moving beams undergoing large-amplitude vibration. The kinematics was formulated in the mixed Eulerian–Lagrangian framework. Based on the kinematic analysis, the governing equations of nonlinear vibration were derived from the extended Hamilton principle and the higher-order shear beam theory. The derivation considered the effects of material parameters on the beam deformation. The proposed governing equations were compared with a few previous governing equations. The comparisons show that proposed equations are with higher precision. Besides, the proposed equations can be viewed as the asymptotic governing equations of Lagrange’s equations of motion for large displacement. Finally, the corresponding boundary conditions and the comparison between the presented model equation and classical model equation were provided.

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Section: Introductionmentioning

confidence: 99%

Kinematic Aspects in Modeling Large-Amplitude Vibration of Axially Moving Beams

Wang

Ding

Chen

2019

Int. J. Appl. Mechanics

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“…The vibration problems of the plate structures in these engineering machines are important for consideration in the design process [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Similitude Design Method of the Distorted Model on Variable Thickness Cantilever Plates

et al. 2016

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Abstract:In the present study, a new method of predicting the dynamic behavior of a variable thickness (VT) cantilever plate by using a thin plate scaled model is proposed. The thin plate model, defined as the model thin (MT) plate, is designed by using the newly proposed similitude design method. The method is derived based on the transfer matrix of both the stepped thickness (ST) plate that is simplified by the VT plate and the thin plate. The thickness of the MT plate is calculated by introducing the equivalent thickness corresponding to each VT plate's vibration modals, such that a series of accurate distorted scaling laws are provided to predict each corresponding property. Moreover, an algorithm of designing the MT plate is proposed and a design process is summarized in steps. Finally, an example, where the prototype VT plate is made of 42 CrMo and the MT plate is made of NO. 45 steel, is discussed to validate the proposed design method, showing that the MT plate, which is designed by using the proposed method, can accurately predict the dynamic properties of the prototype VT plate, and showing its significance in engineering practice.

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“…They studied the viscoelastic effect by perturbing the similar elastic problem and using the method of multiple scales. Very recently, Yang et al studied vibrations, bifurcation, and chaos of axially moving viscoelastic plates using finite differences and a non-linear model for transverse displacements [73].…”

Section: Introductionmentioning

confidence: 99%

The origin of in-plane stresses in axially moving orthotropic continua

Kurki

Jeronen

Saksa

et al. 2016

International Journal of Solids and Structures

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Highlights• In-plane motion of an axially travelling orthotropic sheet was modelled• Velocity difference between supports generates strain due to mass conservation• In a travelling viscoelastic material the axial strain varies along the length• Small deformations of free edges due to the Poisson effect affect the velocity• Inertial effects lead to additional cross-directional contraction AbstractIn this paper, we address the problem of the origin of in-plane stresses in continuous, two-dimensional high-speed webs. In the case of thin, slender webs, a typical modeling approach is the application of a stationary in-plane model, without considering the effects of the in-plane velocity field. However, for high-speed webs this approach is insufficient, because it neglects the coupling between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange-Euler approach in model derivation, the solid continuum problem can be transformed into a solid continuum flow problem. Mass conservation in the flow problem, and the behaviour of free edges in the two-dimensional case, are both seen to influence the velocity field. We concentrate on solutions of a steady-state type, and study briefly the coupled nature of material viscoelasticity and transport velocity in one dimension. Analytical solutions of the one-dimensional equation are presented with both elastic and viscoelastic material models. The two-dimensional elastic problem is solved numerically using a nonlinear finite element procedure. An important new fundamental feature of the model is the coupling of the driving velocity field to the deformation of the material, while accounting for small deformations of the free edges. The results indicate that inertial effects produce an additional contribution to elastic contraction in unsupported, free webs.

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Dynamical analysis of axially moving plate by finite difference method

Cited by 79 publications

References 30 publications

Kinematic Aspects in Modeling Large-Amplitude Vibration of Axially Moving Beams

Kinematic Aspects in Modeling Large-Amplitude Vibration of Axially Moving Beams

Dynamic Similitude Design Method of the Distorted Model on Variable Thickness Cantilever Plates

The origin of in-plane stresses in axially moving orthotropic continua

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