This paper summarized the advances in two transverse models for nonlinear vibration of axially moving beams.Based on a nonlinear model for planar vibration of axially moving beams with coupled transverse and longitudinal motion,the derivation of two nonlinear models of transverse vibration was reviewed.The comparisons between approximate analytical results based on the two models for free,forced and parametric vibration of axially moving beams were surveyed.The deviations of the numerical solutions to the two transverse models from the solution to the coupled equation for different vibrations were also summarized.Some problems for further investigations were discussed.%综述了描述轴向运动梁横向非线性振动的两组数学模型的研究进展.在轴向运动梁径向和横向平面非线性振动耦合模型的基础上,总结了两组横向非线性振动模型的推导,以及在自由振动、受迫振动、参激振动工况下两组横向模型的近似解析比较的研究进展.在直接数值离散方法的基础上,总结了两组横向模型在各种工况下对平面耦合模型近似程度的研究进展.最后提出若干尚待深入研究的问题.
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