Chaotic Properties of Single Element Nonlinear Chimney Model: Effect of Directionality

Abstract

We generalize the chimney model by introducing nonlinear restoring and gravitational forces for the purpose of modeling swaying of trees at high wind speeds. We have derived general equations governing the system using Lagrangian formulation. We have studied the simplest case of a single element in more detail. The governing equation we arrive at for this case has not been studied so far. We study the chaotic properties of this simple building block and also the effect of directionality in the wind on the chaotic properties. We also consider the special case of two elements.