Abstract
In this paper, a spectral element model is derived for the axially moving viscoelastic beams subject to axial tension. The viscoelastic material is represented in a general form by using the one-dimensional constitutive equation of hereditary integral type. The high accuracy of the present spectral element model is verified first by comparing the eigenvalues obtained by the present spectral element model with those obtained by using the conventional finite element model as well as with the exact analytical solutions. The effects of viscoelasticity and moving speed on the dynamics of moving beams are then numerically investigated.
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References
Abolghasemi, M. and Jalali, M. A., 2003, “Attractors of a Rotating Viscoelastic Beam,”International Journal of Non-Linear Mechanics, Vol.38, pp. 739–751.
Christensen, R. M., 1982,Theory of Viscoelasticity. Academic Press, New York.
Dalenbring, M., 2003, “Validation of Estimated Isotropic Viscoelastic Material Properties and Vibration Response Prediction,”Journal of Sound and Vibration, Vol. 265, pp. 269–287.
Doyle, J. F., 1997,Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, Springer-Verlarg, New York.
Findley, W. N., Lai, L. S. and Onarna, K., 1976,Creep and Relaxation of Nonlinear Viscoelastic Materials, New York, North Holland.
Fung, R. F., Huang, J. S. and Chen, Y. C., 1997, “The Transient Amplitude of the Viscoelastic Traveling String: An Integral Constitutive Law,”Journal of Sound and Vibration, Vol. 201, No. 1, pp. 153–167.
Hou, Z. and Zu, J. W., 2002, “Non-linear Free Oscillations of Moving Viscoelastic Belts,”Mechanism and Machines Theory, Vol. 37, pp. 925–940.
Karnovsky, I. A. and Lebed, O. I., 2001,Formulas for Structural Dynamics, McGraw-Hill, New York.
Lee, U. and Lee, J., 1998, “Vibration Analysis of the Plates Subject to Distributed Dynamic Loads by Using Spectral Element Method,”KSME International Journal, Vol. 12, No. 4, pp. 565–571.
Lee, U., Kim, J. and Leung, A. Y. T., 2001, “Vibration Analysis of the Active Multi-Layer Beams by Using Spectrally Formulated Exact Natural Modes,”KSME International Journal, Vol. 15, No. 2, pp. 199–209.
Le-Ngoc, L. and McCallion, H., 1999, “Dynamic Stiffness of an Axially Moving String,”Journal of Sound and Vibration, Vol. 220, No. 4, pp. 749–756.
Marynowski, K. and Kapitaniak, T., 2002, “Kelvin-Voigt versus Burgers Internal Damping in Modeling of Axially Moving Viscoelastic Web,”International Jornal of Non-Linear Mechanics, Vol. 37, pp. 1147–1161.
Oh, H., Lee, U. and Park, D. H., 2004, “Dynamics of an Axially Moving Bernoulli-Euler Beam: Spectral Element Modeling and Analysis,”KSME International Journal, 18 (3), pp. 382–393.
Petyt, M., 1990, Introduction to Finite Element Vibration Analysis, Cambridge University Press, New York.
White, L., 1986, “Finite Element in Linear Viscoelasticity,”Proc. Second Conference on Matrix Method in Structural Mechanics, AFFDL-TR-68-150, pp. 489–516.
Wickert, J. A. and Mote, C. D., 1988, “Current Research on the Vibration and Stability of Axially Moving Materials,”Shock and Vibration Digest, Vol. 20, pp. 3–13.
Zhang, L. and Zu, J. W., 1998, “Non-linear Vibrations of Viscoelastic Moving Belts, Part I and II,”Journal of Sound and Vibration, Vol. 216, No. 1, pp. 75–105.
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Oh, H., Cho, J. & Lee, U. Spectral element analysis for an axially moving viscoelastic beam. KSME International Journal 18, 1159–1168 (2004). https://doi.org/10.1007/BF02983290
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DOI: https://doi.org/10.1007/BF02983290