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中文摘要：
用近似解析方法分析轴向运动黏弹性梁横向非线性受迫振动并通过微分求积方法（DQM）进行数值验证。基于外部存在简谐激励的有限小变形细长梁的非线性模型，用多尺度法建立谐波共振时的可解性条件，进而导出稳态周期响应的幅值及其稳定性。稳定稳态周期解的幅值随外激励幅值的增大而增大，随黏弹性系数或非线性系数的增大而减小。采用微分求积法数值求解描述梁横向运动的非线性偏微分方程。计算结果定性验证了近似解析方法预测的相关参数对稳定稳态周期响应幅值的影响，定量比较表明解析结果有较高精度。
英文摘要：
Forced vibration is investigated for axially moving viscoelastic beams via an approximate analytical method with Differential Quadrature Method （DQM） verification. It is assumed that the excitation is spatially uniform and temporally harmonic. Based on nonlinear models of a slender beam with finite small deformation, a solvability condition is established via the multiple scales method for harmonic resonance. Therefore the amplitudes of steady periodic responses and their stabilities are derived. The amplitudes of stable steady-state responses increase with the amplitude of the excitation, and decrease with the viscous and nonlinear coefficients. The differential quadrature schemes are developed for a nonlinear partial-differential equation to verify the results by multiple scales method. The calculation results confirm qualitatively the effects of the related parameters on the amplitude by approximate analytical prediction. Quantitative comparisons demonstrate that the approximate analysis results are with rather high precision.
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