Detection and Location of Nonlinearities using Reciprocity Breakdown

Damage in a structure often results in local stiffness nonlinearities and detecting these nonlinearities can be used to monitor the health of the structure. It is well-known that nonlinearities in structures lead to a breakdown in reciprocity, where the frequency response function between two points on the structure depends upon the forcing location. This paper proposes a measure to quantify the level of non-reciprocity in a structure and investigates the effect of the location and form of nonlinearity on this non-reciprocity measure. A simulated discrete mass-spring system was used to determine the effect of the excitation and response locations on the ability to detect the nonlinearity. Stepped-sine testing is commonly used to characterise a nonlinear system since harmonic excitation emphasises nonlinear phenomena and can, for example, allow the system to exhibit multiple solutions. Thus, a simulation of a stepped sine test was used as the benchmark to highlight reciprocity breakdown in the most favourable case. However, impact excitation is much easier and faster to implement in practice and consequently the effect of the type of excitation on the detection and location of nonlinearities was considered. Finally, the prospects for using a measure of reciprocity in a structural health monitoring system are discussed.