Modes Coupling Seismic Waves And Vibrating Buildings

Abstract

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 by different author and we able to show the well posedness of this system.Furthermore we show how solving for the wavenumber in a non-linear equation and we are able to find resonant frequencies coupling seismic waves and vibrating tall buildings which ensure the existence seismic risk due to building.