On the limitations of transmissibility functions for damage localisation: the influence of completeness

Transmissibility functions are used to identify and locate damage in critical structures for health monitoring purposes. Their appeal over conventional signal or frequency response-based functions lie in a unique property; sub-structural invariance. It has been shown that the transmissibility of an assembled structure, when obtained correctly, can describe the dynamics of a sub-structure in a manner that is independent from the remainder of the assembly. It is this sub-structural invariance that enables transmissibility functions to locate damage in complex structures. Though a valuable property, sub-structural invariance relies on the notion of a complete interface representation; the interface that separates the sub-structure from the remaining assembly must be sufficiently instrumented so that all important interface dynamics can be captured. In practice, without considerable experimental effort, complete interface representations are not achievable. Importantly, the transmissibilities obtained in the presence of an incomplete interface are unable to discern between damage located interior, or exterior, to a particular sub-structure; they are no longer invariant. Hence, their ability to locate damage is compromised. In the present paper we introduce the notion of completeness in the context of transmissibility-based structural health monitoring, and examine its importance for the accurate localisation of damage through numerical and experimental examples