Numerical investigation into nonlinear parametric resonance of axially accelerating viscoelastic beams
Received:February 20, 2011  Revised:June 15, 2011
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KeyWord:axially moving beam  viscoelasticity  parametric resonance  finite difference method  differential quadrature method
丁虎 上海市应用数学和力学研究所 上海大学, 上海
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      Steady-state responses of transverse parametric vibration of axially accelerating viscoelastic beam with two classical boundary conditions are respectively investigated via two different numerical ways.The governing equation is derived from the viscoelastic constitution relation respectively in terms of material derivative and the partial time derivative.The differential quadrature method is applied directly to the governing equation to determine the steady-state responses of center of the beam due to nonlinear parametric resonance. Numerical simulations show the effects of the two viscoelastic constitutive relations on the steady-state responses.The finite difference schemes are developed to verify results via the method of differential quadrature.Quantitative comparisons demonstrate that the approximate analysis results are with rather high precision.