Dynamic Response of an Axially Moving Viscoelastic Timoshenko Beam

Document Type: Research Paper


School of Mechanical Engineering, University of Shahrood , Shahrood , Islamic Republic of Iran


In this paper, the dynamic response of an axially moving viscoelastic beam with simple supports is calculated analytically based on Timoshenko theory. The beam material property is separated to shear and bulk effects. It is assumed that the beam is incompressible in bulk and viscoelastic in shear, which obeys the standard linear model with the material time derivative. The axial speed is characterized by a simple harmonic variation about a constant mean speed. The method of multiple scales with the solvability condition is applied to dimensionless form of  governing equations in modal analysis and principal parametric resonance. By a parametric study, the effects of velocity, geometry and­ ­viscoelastic­ parameters are investigated on the response.


[1] Chen L.Q., Yang X.D., Cheng C.J., 2004, Dynamic stability of an axially accelerating viscoelastic beam, European Journal of Mechanics - A/Solids 23: 659-666.
[2] Mockensturm E.M., Guo J., 2005, Nonlinear vibration of parametrically excited viscoelastic axially moving strings, Journal of Applied Mechanics 72: 374-380.
[3] Tang Y.Q., Chen L.Q. , Yang X.D., 2009,Nonlinear vibrations of axially moving Timoshenko beams under weak and strong external excitations, Journal of Sound and Vibration 320: 1078-1099.
[4] Chen L.Q., Tang Y.Q., Lim C.W., 2010, Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams, Journal of Sound and Vibration 329: 547-565.
[5] Ding H. , Chen L.Q., 2011, Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams, Acta Mechanica Sinica 27(3): 426-437.
[6] Chen L.Q., Tang Y.Q., 2011, Combination and principal parametric resonances of axially accelerating viscoelastic beams: Recognition of longitudinally varying tensions. Journal of Sound and Vibration 330 (23): 5598-5614.
[7] Ghayesh M., 2011, Nonlinear forced dynamics of an axially moving viscoelastic beam with an internal resonance, International Journal of Mechanical Sciences 53(11): 1022-1037.
[8] Wang B., Chen L.Q., 2012, Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model , Applied Mathematics and Mechanics 33(6): 817-828.
[9] Ghayesh M., Amabili M. , Païdoussis M.P., 2012, Nonlinear vibrations and stability of an axially moving beam with an intermediate spring support: two-dimensional analysis, Nonlinear Dynamics 70: 335-354.
[10] Ghayesh M., Amabili M., Farokhi H., 2013, Coupled global dynamics of an axially moving viscoelastic beam, International Journal of Nonlinear Mechanics 51: 54-74.
[11] Youqi T., 2013, Nonlinear vibrations of axially accelerated viscoelastic Timoshenko beam, Chinese Journal of Theoretical and Applied Mechanics 45 (6): 965-973.
[12] Riandeh E., Calleja R.D., Prolongo M.G. , 2000, Polymer Viscoelasticity: stress and Strain in Practice, Marcel Dekker Inc., New York.
[13] Brinson H.F., Brinson L.C., 2008, Polymer Engineering Science and Viscoelasticity: an Introduction, Springer Science Business Media, LLC, New York.
[14] Rao S.S., 2007, Vibration of Continues Systems, John Wiley, New Jersey.
[15] Roylance D., 2001, Engineering Viscoelasticity, Massachusetts Institute of Technology, Cambridge, Department of Material Science and Engineering.
[16] Nayfeh A.H., 1993, Introduction to Perturbation Techniques, John Wiley, New York.
[17] Seddighi H., Eipakchi H.R., 2013, Natural Frequency and Critical Speed Determination of an Axially Moving Viscoelastic Beam, Mechanics of Time-Dependent Materials 17:529-541.