Dynamic stability of an axially accelerating viscoelastic beam

Shanghai University, Shanghai, Shanghai Shi, China
European Journal of Mechanics - A/Solids (Impact Factor: 1.68). 07/2004; 23(4):659-666. DOI: 10.1016/j.euromechsol.2004.01.002


This work investigates dynamic stability in transverse parametric vibration of an axially accelerating viscoelastic tensioned beam. The material of the beam is described by the Kelvin model. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The Galerkin method is applied to discretize the governing equation into a infinite set of ordinary-differential equations under the fixed–fixed boundary conditions. The method of averaging is employ to analyze the dynamic stability of the 2-term truncated system. The stability conditions are presented and confirmed by numerical simulations in the case of subharmonic and combination resonance. Numerical examples demonstrate the effects of the dynamic viscosity, the mean axial speed and the tension on the stability conditions.

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Available from: Li-Qun Chen, Oct 06, 2015
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    • "The dynamics of these systems is studied in two sub-and super-critical axial velocity regimes, the critical velocity is the limit between these two regimes, in which instability occurs. On the other hand, axial velocity fluctuations could cause instabilities even in a very low axial velocity [7] [8] [9] [10] [11] [12] [13]. Pakdemirli and Ulsoy [14] studied the parametric principal resonance and combination resonance for any two modes of axially moving string. "
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    ABSTRACT: The extraordinary properties of carbon nanotubes enable a variety of applications such as axially moving elements in nanoscale systems. For vibration analysis of axially moving nanoscale beams with time-dependent velocity, the small-scale effects could make considerable changes in the vibration behavior. In this research, by applying the nonlocal theory and considering small fluctuations in the axial velocity, the stability and non-linear vibrations of an axially moving nanoscale visco-elastic Rayleigh beam are studied. It is assumed that the non-linearity is geometric and is due to the axial stress changes. The energy loss in the system is considered by using the Kelvin-Voigt model. The governing higher order nonlocal equation of motion is derived by using the Hamilton's principle and is analyzed by applying the multiple scales and power series methods. Then the non-linear resonance frequencies and response of the system are obtained. Considering the solvability condition, the stability of the system is studied parametrically through the Lyapunov's first method. An interesting result is that, considering the small-scale effects changes the slope of the frequency response curves due to the fluctuations in the axial velocity, considerably.
    International Journal of Mechanical Sciences 03/2015; 96-97:36-46. DOI:10.1016/j.ijmecsci.2015.03.017 · 2.03 Impact Factor
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    • "In addition to elastic beams, axially accelerating viscoelastic beams have recently been investigated. Chen, Yang and Cheng (2004) applied the averaging method to a discretized system via the Galerkin method to present analytically the stability boundaries of axially accelerating viscoelastic beams with clamped-clamped ends. Chen and Yang (2005) applied the method of multiple scales without discretization to obtain analytically the stability boundaries of axially accelerating viscoelastic beams with pinned-pinned or clamped-clamped ends. "
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    • "Stability boundaries were investigated for different boundary conditions. The method of averaging was applied to the 2-term Galerkin truncation of the equation of motion of axially accelerating viscoelastic beam by Chen et al. [21]. "
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    ABSTRACT: Linear models of axially moving viscoelastic beams and viscoelastic pipes conveying fluid are considered. The natural frequencies of the models are calculated. For both models, viscoelasticity terms are assumed to be of order one. Natural frequencies corresponding to various beam and pipe parameters are presented. Effects of viscoelasticity on the natural frequencies are discussed.
    Advances in Mechanical Engineering 04/2013; 2013. DOI:10.1155/2013/169598 · 0.58 Impact Factor
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