Localisation and curve veering: A different perspective on modal interactions

The interaction of vibration modes subject to parametric variation has long been observed to cause curious effects, notably those of localisation and frequency curve veering. These phenomena have great significance in practical applications: localisation is responsible for unexpectedly high levels of response in periodic structures, for example in turbine rotor assemblies, and frequency curve veering has shown correlation with a variety of critical behaviours, for example in the stability analysis of helicopter vibrations. This paper presents an in-depth analysis of the behaviour and derives new system properties with respect to parameter perturbations. The properties offer a different perspective on the interaction of vibration modes and the fresh insight is demonstrated with reference to some example problems. The paper details how the approach will lead to optimisations in existing computational algorithms and examples are given. Two normalised criteria are suggested to standardise the approach to such problems. Combining these criteria produces a veering index which is proposed as a definitive measure of the presence and intensity of curve veering.