Abstract

Quarter car models of vehicles rolling on wavy roads lead to limit cycles of travel speed and acceleration with period doublings and bifurcation effects for appropriate driving force parameters. In case of narrow-banded road excitations, speed jumps occur, additionally. This has the consequence that the driving speed becomes turbulent. Bifurcation and jump effects vanish with growing vehicle damping. The same happens for increasing bandwidth of road excitations when, e.g., on flat highways there are no big road waves but only small noisy slope processes generated by rough road surfaces. The paper derives a new stability condition in mean. Numerical time integrations are stabilized by means of polar coordinates. Equivalently, Fourier series expansions are introduced in the angle domain. Phase portraits of travel speed and acceleration show new period-doublings of limit cycles when speed gets stuck before resonance. The paper extends these investigations to the stochastic case that road surfaces are random generated by filtered white noise. By means of Gaussian closure, a nonlinear mean speed equation is derived which includes the extreme cases of wavy roads and road noise.

中文翻译：

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非线性车辆动力学中的湍流行驶速度

摘要

在波浪状道路上滚动的车辆的四分之一汽车模型会导致行驶速度和加速度的极限循环，其中周期倍增和分叉效应适用于适当的驱动力参数。在窄带道路激励的情况下，还会发生速度跳跃。结果是行驶速度变得紊乱。随着车辆阻尼的增加，分叉和跳跃效应消失。当例如在平坦的高速公路上没有大的道路波而是只有由粗糙路面产生的小的嘈杂的斜坡过程时，对于增加道路激励的带宽也会发生同样的情况。本文推导了一个新的均值稳定条件。数值时间积分通过极坐标来稳定。等效地，在角域中引入了傅立叶级数展开。当速度在共振之前卡住时，行驶速度和加速度的相图显示了极限循环的新周期倍增。本文将这些研究扩展到随机情况下，即由滤波后的白噪声随机产生的路面。通过高斯封闭，推导了非线性平均速度方程，其中包括波浪状道路和道路噪声的极端情况。