Calculation of eigensensitivity is usually time-consuming for a large-scale structure. This paper develops a substructuring method for computing the first, second and high order eigensensitivity.The local area of a structure is treated as an independent substructure to be analyzed. The eigensensitivity of global structure with respect to a design parameter are calculated from the eigensensitivity of a particular substructure that contains the design parameter, thus allowing a significant reduction in computational cost. The accuracy and efficiency of the substructuring method is proved by a frame structure and a highway bridge.
In traditional structural damage identification methods, it is usually time consuming to identify a large number of unknown parameters on a large-scale structure. This paper proposes a substructural method to identify the local damage of the large and complex systems. The structural damage, the external moving force and interface forces of adjacent substructures are identified simultaneously from the measured dynamic acceleration responses. The dynamic response sensitivities with respect to the structural parameters and the orthogonal factors of the moving force and interface forces are derived in the state space domain. The proposed method is verified by a simple supported beam and a three-storey frame. Numerical results have shown that the external force, interface force and the structural local damages can be identified by the proposed method effectively and efficiently. Since the concerned substructure is independent and the interface from remaining substructures can be identified, the concerned substructure can be singled out to be used for a large number of substructural analysis.
The traditional deterministic damage detection method is based on the assumption that the measured data and the finite element model are accurate. However, in real situation, there are many uncertainties in the damage identification procedure such as the errors of the finite element model and the measurement noise. Since the uncertainties inevitably exist in the finite element models and measured data, the statistic method which considers the uncertainty has wide practical application. This paper proposes a statistical damage identification method based on dynamic response sensitivity in state-space domain. Considering the noise of the finite element model and measured acceleration response, the statistical variations of the damaged finite element model are derived with perturbation method which is based on a Taylor series expansion of the response vector and verified by Monte Carlo technique. Afterward, the probability of damage existence for each structural element is estimated using the statistical characteristic of the identified structural parameters. A numerical simply supported beam under the moving load is applied to demonstrate the accuracy and efficiency of the proposed statistical method.
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