Abstract
In this article, we proposed and analyzed a mathematical model for the so – called city – effect in what in which an earthquake can be locally disturbed by the collective response of tall buildings in the large city. We use a set of equations c0upling vibrations buildings in buildings to motion under the ground. These equations were previously studied by different authors the existence of the seismic wave was ensured by a method of Numerical solutions. None those authors do not consider differential methods to show the existence of earthquake due to tall buildings. Furthermore, we show how we can solve for the wavenumber in a non – linear equation and we are able to find resonant frequencies coupling seismic waves and vibrating tall building which ensure the existence seismic wave due to building.
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