Model updating of periodic structures based on free wave characteristics

Many civil engineering structures have a repetitive or quasi-periodic geometry. Such structures have clustered modes with closely spaced natural frequencies corresponding to mode shapes with similar wavelengths. Such modes may be difficult to distinguish in modal tests and lead to difficulties when pairing calculated and experimentally determined modal characteristics in vibration-based model updating. For repetitive structures, the free wave characteristics, i.e. propagation constants and free waves, can be used alternatively to characterize their dynamic behaviour. The free wave characteristics can therefore be used instead of modal characteristics as data features in model updating of repetitive structures. This paper investigates the feasibility of model updating of repetitive structures based on free wave characteristics. First, the identification of the free wave characteristics from the measured vibration responses of a periodic structure is investigated. A stabilization diagram is constructed to pick up the stable free waves. Second, model updating of repetitive structures is performed through a match of the calculated and experimentally identified free wave characteristics. A least-squares cost function is formulated and minimized using a gradient-based optimization algorithm. This algorithm requires the sensitivity of the free wave characteristics to the model parameters that need to be updated. The analytical expressions for the free wave sensitivities are therefore derived. The proposed model updating procedure is demonstrated and validated by a numerical case study involving a repetitive frame structure and by an experiment on a four-storey steel frame structure. The results confirm the feasibility of model updating based on free wave characteristics for repetitive structures.