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Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (6): 817-828.doi: https://doi.org/10.1007/s10483-012-1588-8

• 论文 • 上一篇    

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

王波   

  1. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 200235, P. R. China
  • 收稿日期:2011-05-09 修回日期:2012-02-29 出版日期:2012-06-10 发布日期:2012-06-10
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (No. 10972143), the Shanghai Municipal Education Commission (No. YYY11040), the Shanghai Leading Academic Discipline Project (No. J51501), the Leading Academic Discipline Project of Shanghai Institute of Technology (No. 1020Q121001), and the Start Foundation for Introducing Talents of Shanghai Institute of Technology (No. YJ2011-26)

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

Bo WANG   

  1. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 200235, P. R. China
  • Received:2011-05-09 Revised:2012-02-29 Online:2012-06-10 Published:2012-06-10
  • Contact: Bo WANG E-mail:b.wang@live.com
  • Supported by:

    Project supported by the National Natural Science Foundation of China (No. 10972143), the Shanghai Municipal Education Commission (No. YYY11040), the Shanghai Leading Academic Discipline Project (No. J51501), the Leading Academic Discipline Project of Shanghai Institute of Technology (No. 1020Q121001), and the Start Foundation for Introducing Talents of Shanghai Institute of Technology (No. YJ2011-26)

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摘要： The weakly forced vibration of an axially moving viscoelastic beam is investigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of nontrivial steady-state response is examined via the Routh-Hurwitz criterion.

关键词: axially moving beam, weakly forced vibration, standard linear solid model, method of multiple scales, steady-state response

Abstract: The weakly forced vibration of an axially moving viscoelastic beam is investigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of nontrivial steady-state response is examined via the Routh-Hurwitz criterion.

Key words: axially moving beam, weakly forced vibration, standard linear solid model, method of multiple scales, steady-state response

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