Modeling of Nonlinear Oscillations for Viscoelastic Moving Belt Using Generalized Hamilton’s Principle

Chen, Li‐Hui; Zhang, W.; Liu, Y. Q.

doi:10.1115/1.2346691

Cited by 52 publications

(30 citation statements)

References 15 publications

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“…Actually, the standard linear solid model, which can describe the behavior of linear viscoelastic materials of solid type with limited creep deformation, covers the Kelvin model and the integral-type constitution relation with an exponential relaxation function as special cases. When differential-type constitutive laws are incorporated, some investigators used the partial time derivative in the viscoelastic constitutive relations [2][3][4][6][7][8]11,12,14,15,20,21,23,24]. However, Mochensturm and Guo [18] demonstrated that the material time derivative should be used to account for the additional "steady state" dissipation of an axially moving viscoelastic string.…”

Section: Introductionmentioning

confidence: 97%

Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model

Chen

Chen²

2009

J Eng Math

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Nonlinear parametric vibration of axially accelerating viscoelastic strings is investigated via an approximate analytical approach. The standard linear solid model using the material time derivative is employed to describe the string viscoelastic behaviors. A coordinate transformation is introduced to derive Mote's model of transverse motion from the governing equation of the stationary string. Mote's model leads to Kirchhoff's model by replacing the tension with the averaged tension over the string. An asymptotic perturbation approach is proposed to study principal parametric resonance based on the two models. The amplitude and the existence conditions of the steady-state responses are determined by locating the nonzero fixed points in the modulation equations resulting from the solvability condition. Numerical results are presented to highlight the effects of the material parameters, the axial-speed fluctuation amplitude, and the initial stress on steady-state responses.

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Section: Introductionmentioning

confidence: 97%

Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model

Chen

Chen²

2009

J Eng Math

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“…Different models have been exploited to express the constitutive relations of the homogeneous viscoelastic materials such as the differential models, Chen et al (2007), Boltzmann superposition integral model, Hamed (2012) and Lei et al (2013a, b) or fractional viscoelasticity models, Ezzat et al (2013) and Ansari et al (2015Ansari et al ( , 2016. On the other side, many papers adopted the correspondence principle and Laplace transformation methods such as Kiasat et al (2014) and Khazanovich (2008).…”

Section: Introductionmentioning

confidence: 99%

Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects

Attia

Mahmoud

2016

Int J Mech Mater Des

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The present study introduces an analytical-computational model to simulate the effects of different simultaneous aspects on the behavior of nanobeams. The first one deals with the space nonlocality interaction and taking into account the microstructure effects, which has been formulated by using the nonlocal couple-stress elasticity. The second factor deals with the memory-dependent effect and has been investigated in the framework of linear viscoelasticity theory. It is the first time to apply the coupled effects of the microstructure and long-range interactions between the particles, to reflect the sizedependency of viscoelastic structures. BernoulliEuler nanobeam is taken as a vehicle to present the details of the proposed model. Eringen nonlocal elasticity and the modified couple-stress theory are used to formulate the two phenomena of long-range cohesive interaction and the microstructure local rotation effects, respectively. Boltzmann superposition viscoelastic model, endowed by Wiechert series, is used to simulate the linear behavior of isotropic, homogeneous and non-aging viscoelastic materials. The extended Hamilton's principle is applied to formulate the analytical model of mechanical behavior of the nonlocal couple-stress nanobeam. The model has been verified and some results are compared with those published in the literature and a good agreement has been obtained. It is shown that the material-length scale parameter, nonlocal parameter, viscoelastic relaxation time and length-to-thickness ratio have a significant effect on the bending response of viscoelastic nanobeams with various boundary conditions.

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“…Recently, different nonlinear models of transverse vibration of axially moving strings were adopted to investigate energetics and conserved quantities [10,11]. Besides, governing equations can be derived from the energy principle [12]. The conserved quantities were applied to check numerical schemes [13][14][15] and to analyze the stability [11].…”

Section: Introductionmentioning

confidence: 99%

Energetics and conserved quantity of an axially moving string undergoing three-dimensional nonlinear vibration

2007

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Nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings. The time-rate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way. For a string moving in a constant axial speed and constrained by two fixed ends, a conserved quantity is proved to remain unchanged during three-dimensional vibration, while the string energy is not conserved. An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration. Numerical simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mechanical energy and the invariance of the conserved quantity.

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Modeling of Nonlinear Oscillations for Viscoelastic Moving Belt Using Generalized Hamilton’s Principle

Cited by 52 publications

References 15 publications

Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model

Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model

Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects

Energetics and conserved quantity of an axially moving string undergoing three-dimensional nonlinear vibration

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