振荡电桥中的非线性
Nonlinearity in oscillating bridges
摘要：
我们首先回顾几个历史上的摆动桥梁，在某些情况下，导致崩溃。其中一些是最近的，并表明，如今，在悬索桥的振荡还没有得到很好的理解。接下来，我们调查一些尝试模型桥梁与微分方程。虽然这些方程来自不同的科学团体，但它们显示出一些共同的特征。其中之一，我们认为是不正确的，是接受的线性虎克定律的弹性。该定律仅适用于偏离平衡点较小的情况，这种情况在强烈振动的桥梁中不会发生。然后，我们讨论了最近的几个模型，其解决方案表现出自激振荡，在真正的桥梁中可见的现象。这表明了一个不同的观点，在建模方程，并给出了一个强有力的提示，如何修改现有的模型，以获得一个可靠的理论。本文的目的正是为了强调重温经典模型的必要性，介绍可靠的模型，并指出我们认为达到这一目标所必需的步骤。
英文摘要：
We first recall several historical oscillating bridges that, in some cases, led to collapses. Some of them are quite recent and show that, nowadays, oscillations in suspension bridges are not yet well understood. Next, we survey some attempts to model bridges with differential equations. Although these equations arise from quite different scientific communities, they display some common features. One of them, which we believe to be incorrect, is the acceptance of the linear Hooke law in elasticity. This law should be used only in presence of small deviations from equilibrium, a situation which does not occur in strongly oscillating bridges. Then we discuss a couple of recent models whose solutions exhibit self-excited oscillations, the phenomenon visible in real bridges. This suggests a different point of view in modeling equations and gives a strong hint how to modify the existing models in order to obtain a reliable theory. The purpose of this paper is precisely to highlight the necessity of revisiting classical models, to introduce reliable models, and to indicate the steps we believe necessary to reach this target.
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