### Preprint

Hinke M. Osinga

**Abstract**

Failure of structures in an earthquake is an important problem that is still not well understood. We investigate how an external force with varying magnitude and principal frequency affects structurural stability. As an example we consider the analytical model of a tied rocking block on an elastic foundation, which exhibits dynamics equivalent to that of a planar, post-tensioned frame on a shake table; here, we consider a periodic external force, but our goal is to predict behaviour of models subject to an aperiodic external force (an earthquake). A standard approach would be to run a large number of simulations over a range of magnitudes and frequencies. We compute the failure boundary directly and find that failure can occur in profoundly different ways. Inherent nonlinearities in the system can have dramatic effects on the stability of the structure, especially when it has a natural frequency close to that of the external forcing.

**PDF** copy of the paper (323KB)

Created by Hinke Osinga

Last modified: Sat Feb 11 15:50:00 NZDT 2017