The phenomenon of edge-buckling in an axially moving stretched thin elastic web is described as a nonstandard singularly perturbed bifurcation problem, which is then explored through the application of matched asymptotic techniques. Previous numerical work recently reported in the literature is reevaluated in this context by approaching it through the lens of asymptotic simplifications. This allows us to identify two distinct regimes characterised by qualitative differences in the corresponding eigendeformations; some simple approximate formulae for the critical eigenvalues are also proposed. The obtained analytical results capture the intricate relationship between the critical speeds, the background tension, and other relevant physical and geometric parameters that feature in the mathematical model.

轴向移动拉伸薄弹性网中的边缘屈曲现象被描述为非标准奇扰动分岔问题，然后通过应用匹配渐近技术对其进行探索。最近在文献中报道的先前的数值工作在这种背景下通过渐近简化的视角进行了重新评估。这使我们能够识别出两种不同的机制，其特征是相应特征变形的质量差异；还提出了一些简单的临界特征值的近似公式。获得的分析结果捕捉了数学模型中的临界速度、背景张力以及其他相关物理和几何参数之间的复杂关系。