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中文摘要：
本文研究了黏弹性轴向运动梁横向受迫振动稳态幅频响应问题。在控制方程的推导中，对黏弹性本构关系采用物质导数。把多尺度法直接应用于梁横向振动的非线性控制方程，利用可解性条件消除长期项，得到系统稳态的幅频响应曲线。运用Lyapunov一次近似理论分析幅频响应曲线的稳定性。通过算例研究了黏性系数，外部激励幅值以及非线性项系数对稳态幅频响应曲线及其稳定性的影响。运用数值方法对两端固定边界下黏弹性轴向运动梁的控制方程直接数值解，分析梁横向非线性振动的稳态幅频响应，通过数值算例验证直接多尺度法的结论。
英文摘要：
Forced vibration was investigated for axially moving viscoelastic beams. The governing equation was derived from the viscoelastic constitution relation by using material derivative. The method of multiple scales was applied to the mathematical model to calculate the steady state response. The equation of response curves was derived from the solvability condition of eliminating secular terms. The stability of steady state responses was analyzed by use of Lyapunov linearized stability theory. The finite difference schemes were developed to solve the equation of axially moving viscoelastic beams with fixed supports for steadystate response. Numerical examples are presented to highlight the effects of non - linear coefficient, the excitation amplitude, and viscosity coefficient.
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