Dynamic finite element analysis applied to a simple model exhibiting dynamic instability

Abstract

The paper desribes an energy‐based framework for a simple model with two degrees‐of‐freedom that statically exhibits bifurcations or limit‐points. Dynamically, the equivalent system may respond with small amplitude motion (being dynamically stable) or it may ‘escape’ and move to exhibit ‘large amplitude motion’ (thus becoming dynamically unstable). The energy framework is used to define bounds for these stable and unstable motions. These bounds are used to provide a framework for a set of dynamic finite element computations based on conventional finite element techniques.