地震波与高层建筑振动耦合的优选频率
Preferred Frequencies for Coupling of Seismic Waves and Vibrating Tall Buildings
摘要：
我们研究了一个所谓的“城市效应”的模型，在这个模型中，地震可以通过大城市中高层建筑的集体响应而局部增强。我们用一组方程把建筑物的振动和地下的运动耦合起来。这些方程以前专门研究的情况下，有限集的相同，等距，建筑物。这两个限制在本文中被取消。我们现在可以模拟涉及无限多个建筑物的几何形状，只要建筑物的初始模式重复即可。我们的新方法使用周期域和周期格林函数产生更快的计算。这就是为什么我们现在能够研究可变高度、质量和刚度的建筑物系统的主要原因。我们展示了如何求解一个非线性方程中的波数，该非线性方程涉及到一个适当的积分方程的函数解的积分，我们能够找到耦合地震波和振动的高层建筑物的共振频率。有趣的是，在不相同的建筑物的情况下，我们的模拟表明，这种耦合现象的反应可能会有很大的不同，从一个建筑物到另一个。
英文摘要：
We study a model for the so called "city effect" in which an earthquake can be locally enhanced by the collective response of tall buildings in a large city. We use a set of equations coupling vibrations in buildings to motion under the ground. These equations were previously studied exclusively in the case of a finite set of identical, equally spaced, buildings. These two restrictions are lifted in this paper. We may now simulate geometries involving infinitely many buildings as long as an initial pattern of buildings is repeated. Our new method using periodic domains and periodic Green's functions yields much faster computations. This is the main reason why we are now able to study systems of buildings of variable height, mass, and rigidity. We show how solving for the wavenumber in a non-linear equation involving the integral of a function solution to an adequate integral equation, we are able to find resonant frequencies coupling seismic waves and vibrating tall buildings. Interestingly, in the case of non identical buildings, our simulations indicate that the response to this coupling phenomenon may differ drastically from one building to another.
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