  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.
