Affordable Access

Publisher Website

Existence of frequency modes coupling seismic waves and vibrating tall buildings

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Identifiers
DOI: 10.1016/j.jmaa.2014.07.008
Keywords
  • Applied Mathematics

Abstract

Abstract 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 conditions 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 their existence. This is what this present study offers to provide.

There are no comments yet on this publication. Be the first to share your thoughts.