搓衣板道路建模：从实验测量到线性稳定性分析
Modelling Washboard Road: from experimental measurements to linear stability analysis
摘要：
当车辆反复通过时，由沙子或砾石制成的未铺砌道路会形成波纹状，称为搓板或波纹路。我们提出了一个稳定性分析的基础上，实验测量的力作用在叶片（或犁）拖在一个圆形的砂轨道，并表明，一个线性模型足以描述发病附近的不稳定性。通过试验研究了犁体运动轨迹与犁体通过后留下的沙床剖面之间的关系。通过在最初平坦的砂床上对叶片施加正弦轨迹以及通过在最初波纹状的砂床上施加水平轨迹来确定犁上的颗粒材料流所产生的升力的表达式中的各个项。我们的模型恢复了所有以前观察到的洗衣板路的功能，并准确地预测了最不稳定的波长附近的发病以及不稳定的临界速度。
英文摘要：
When submitted to the repeated passages of vehicles unpaved roads made of sand or gravel can develop a ripply pattern known as washboard or corrugated road. We propose a stability analysis based on experimental measurements of the force acting on a blade (or plow) dragged on a circular sand track and show that a linear model is sufficient to describe the instability near onset. The relation between the trajectory of the plow and the profile of the sand bed left after its passage is studied experimentally. The various terms in the expression of the lift force created by the flow of granular material on the plow are determined up to first order by imposing a sinusoidal trajectory to the blade on an initially flat sand bed, as well as by imposing a horizontal trajectory on an initially rippled sand bed. Our model recovers all the previously observed features of washboard road and accurately predicts the most unstable wavelength near onset as well as the critical velocity for the instability.
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