We investigated the dynamic equilibrium of various structural systems in the previous chapters. Now we consider a very important property of systems in equilibrium, namely, their stability. Our intuitive notion of stability is that small perturbations of a system (which are always present in real situations) only cause the system to have small motions about its (dynamic) equilibrium configuration. If the small perturbations cause motions that are excessive, we talk of an instability of the motion. Some situations where the stability of the motion arises are aeroelastic flutter, whirling of shafts, rotating saw blades and computer disks, belt drives, galloping of power lines, and control of structures.

Underlying this is the idea of a dynamic equilibrium position; although the system is in motion, it is stable in the sense that any disturbance eventually dies down, and the system returns to that dynamic state. This is a concept we make clear at the beginning.

In truth, instability is a nonlinear dynamic phenomenon because we are talking of structural behavior changing – the system is in one state and then moves to another. This new state could be near or far (in the phase-plane sense), and that informs the nature of the instability. Thus we also need to make clear the difference between the initiator of the instability and where the system goes.

Some Preliminary Stability Ideas

Central to the idea of instability is the concept of an unfolding parameter.