地震波与高层建筑振动耦合频率模式的存在性
Existence of Frequency Modes Coupling Seismic Waves and Vibrating Tall Buildings
摘要：
本文证明了地震波与高层建筑振动耦合的频率模态的存在性结果。在以前的研究中，从物理原理推导出了一组模拟这种现象的方程。在该模型中，所有的振动都被假定为反平面和时间谐波，因此可以使用二维Helmholtz方程。一旦我们可以确定一个波数，使得下半平面中相应的Helmholtz方程的解与界面处的相关Neumann和Dirichlet满足理想化高层建筑底部的特定积分方程，就可以获得耦合频率模式。虽然数值模拟表明这样的波数应该存在，但据我们所知，迄今为止，还没有理论上的证据。这就是本研究所提供的。
英文摘要：
We prove in this paper an existence result for frequency modes coupling seismic waves and vibrating tall buildings. The derivation from physical principles of a set of equations modeling this phenomenon was done in previous studies. In this model all vibrations are assumed to be anti plane and time harmonic so the two dimensional Helmholtz equation can be used. A coupling frequency mode is obtained once we can determine a wavenumber such that the solution of the corresponding Helmholtz equation in the lower half plane with relevant Neumann and Dirichlet at the interface satisfies a specific integral equation at the base of an idealized tall building. Although numerical simulations suggest that such wavenumbers should exist, as far as we know, to date, there is no theoretical proof of existence. This is what this present study offers to provide.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
