  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.
