This thesis presents a method of localized health monitoring based on an invariance property of transmission zeros of substructural frequency response functions. The proposed method has several desirable characteristics which make it attractive for use in damage detection applications. These are the independence from initial parameter estimates, the determination of a unique damage location, and the fact that the method is particularly suited for structural continuum applications where other methods perform poorly.; The proposed method is based on a substructuring technique for structural mechanics. The structural equations of motion are cast in a variational framework and are mathematically decomposed into substructures using Lagrange multipliers as boundary constraints. The global dynamics of the system are then written in terms of the independent dynamics of each substructure plus the inter-element dynamics. The frequency response functions of the localized form represent the energy transfer between unique input forces which are derived from the total global force input and output variables which exist independently on a substructure. Because transmission zeros are highly dependent on the input and output of the system under consideration, they exhibit different characteristics in the local form versus the global form.; If damage is limited to a change in flexibility, then it can be shown that the transmission zeros of a partition of the full transfer function matrix corresponding to a damaged substructure are invariant to the damage. Transmission zeros of partitions of the transfer function matrix corresponding to healthy substructures likewise can be shown to vary with the damage. Identification of the substructure whose zeros exhibit the least amount of variation between tests results in identification of the damage location.; Analytical and experimental examples are used to demonstrate the theory and abilities of the proposed method. In each example, the system frequency response is computed from measured input and output signals. System realization is performed to determine the modal parameters of the system. An equivalent state-space representation of the model is determined, and this model is then localized based on an underlying assumed connectivity. The transmission zeros of partitions of the given localized system are computed, and their variations are compared to determine the location of damage.
展开▼
