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

作　　者：王波 

机构地区：[1]School of Mechanical Engineering,Shanghai Institute of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2012年第6期817-828,共12页应用数学和力学（英文版）

基　　金：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);the Start Foundation for Introducing Talents of Shanghai Institute of Technology (No.YJ2011-26)

摘　　要：The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. 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 non- trivial steady-state response is examined via the Routh-Hurwitz criterion.The weakly forced vibration of an axially moving viscoelastic beam is inves- tigated. 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 non- trivial 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 

分 类 号：O326[理学—一般力学与力学基础]