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Parametric resonance of axially moving Timoshenko beams with time-dependent speed

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Abstract

In this paper, parametric resonance of axially moving beams with time-dependent speed is analyzed, based on the Timoshenko model. The Hamilton principle is employed to obtain the governing equation, which is a nonlinear partial-differential equation due to the geometric nonlinearity caused by the finite stretch of the beam. The method of multiple scales is applied to predict the steady-state response. The expression of the amplitude of the steady-state response is derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by using the Lyapunov linearized stability theory. Some numerical examples are presented to demonstrate the effects of speed pulsation and the nonlinearity in the first two principal parametric resonances.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai, 200072, China

    You-Qi Tang & Li-Qun Chen

  2. Department of Mechanics, Shanghai University, Shanghai, 200436, China

    Li-Qun Chen

  3. Department of Engineering Mechanics, Shenyang Institute of Aeronautical Engineering, Shenyang, 110034, China

    Xiao-Dong Yang

Authors
  1. You-Qi Tang
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  2. Li-Qun Chen
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  3. Xiao-Dong Yang
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Correspondence to Li-Qun Chen.

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Tang, YQ., Chen, LQ. & Yang, XD. Parametric resonance of axially moving Timoshenko beams with time-dependent speed. Nonlinear Dyn 58, 715–724 (2009). https://doi.org/10.1007/s11071-009-9512-1

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  • DOI: https://doi.org/10.1007/s11071-009-9512-1

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