The idea of negative stiffness might appear at first glance to be counter intuitive but that is what happens often to machinery in the real world. When such a phenomenon strikes, it triggers rapid deterioration of a machinery system.
Positive stiffness is a material property that tries to resist a force when applied on to a material, i.e. it tries to push back the force.
On the other hand, negative stiffness is a property that amplifies the deformation of a material when force is applied to a body.
Since such amplification is non-linear by nature it forces the system to go far away from its equilibrium position. When it does so, the system become unstable and as deformation quickly increases, the system fails.
The best possible way to detect the sudden appearance of negative stiffness is to monitor the displacement parameter of vibration. This is because displacement is related to stiffness. When displacement increases disproportionately without a corresponding increase in velocity parameter we would know that the phenomenon is that of negative stiffness. In addition, we might also notice a variation in the displacement readings. They don’t tend to settle to a steady state.
Negative stiffness might occur in many ways. It may happen when interference or push fitted elements come loose. It often happens to elements that are deformed over time like foundation supports or are pre-stressed like anti-friction bearings. It might happen when elements are worn out by a certain extent by different wear processes like corrosion or abrasive wear.
But in all cases, a very small change induces a system with positive stiffness to flip to negative stiffness, causing catastrophic damages and failures.
For a lucid understanding of the nature of negative stiffness you may refer to this article.
For an understanding of negative stiffness and isolation you may see this.