WANG Bo. Asymptotic Analysis on Weakly Forced Vibration of an Axially Moving Viscoelastic Beam Constituted by Standard Linear Solid Model[J]. Applied Mathematics and Mechanics, 2012, 33(6): 771-780. doi: 10.3879/j.issn.1000-0887.2012.06.010
 Citation: WANG Bo. Asymptotic Analysis on Weakly Forced Vibration of an Axially Moving Viscoelastic Beam Constituted by Standard Linear Solid Model[J]. Applied Mathematics and Mechanics, 2012, 33(6): 771-780.

# Asymptotic Analysis on Weakly Forced Vibration of an Axially Moving Viscoelastic Beam Constituted by Standard Linear Solid Model

##### doi: 10.3879/j.issn.1000-0887.2012.06.010
• Rev Recd Date: 2012-02-29
• Publish Date: 2012-06-15
• The weakly forced vibration of an axially moving viscoelastic beam was investigated. The viscoelastic material of beams was constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration were derived from dynamical, constitutive, and geometrical relations. The method of multiple scales was applied to determine the steady-state response. The modulation equation was derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response were derived from the modulation equation. The stability of nontrivial steadystate response was examined via RouthHurwitz criterion.
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