Asymptotic Analysis on Weakly Forced Vibration of an Axially Moving Viscoelastic Beam Constituted by Standard Linear Solid Model
摘要: 研究了轴向运动三参数黏弹性梁的弱受迫振动．建立了轴向运动三参数黏弹性梁受迫振动的控制方程．使用多尺度法渐近分析了运动梁的稳态响应，导出了解稳定性边界方程、稳态振幅的表达式以及稳态响应非零解的存在条件．依据Routh-Hurwitz定律决定了非线性稳态响应非零解的稳定性．Abstract: 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 steadystate response was examined via RouthHurwitz criterion.
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