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SUMMARYStructural pounding during earthquakes has been recently investigated extensively by using different models of impact force. In this paper, reexamination of the Hertz contact model with nonlinear damping is made. Based on this reexamination, the formula used to determine the damping constant in terms of the spring stiffness, the coefficient of restitution and relative approaching velocity of two colliding bodies is found to be incorrect for pounding simulation in structural engineering. In order to correct this problem, a more accurate approximating formula for the damping constant is theoretically derived. The correctness of the derived analytical formula has been confirmed through numerical simulations.

Piezoelectric lead zirconate titanate (PZT) is being gradually applied into practice as a new intelligent material for structural health monitoring. In order to study the damage detection properties of PZT on concrete slabs, simply supported reinforced concrete slabs with piezoelectric patches attached to their surfaces were chosen as the research objects and the Electromechanical Impedance method (EMI) was adopted for research. Five kinds of damage condition were designed to test the impedance values at different frequency bands. Consistent rules are found by calculation and analysis. Both the root mean square deviation (RMSD) and the correlation coefficient deviation (CCD) damage indices are capable of detecting the structural damage. The newly proposed damage index Ry/Rx can also predict the changes well. The numerical and experimental studies verify that the Electromechanical Impedance method can accurately predict changes in the amount of damage in reinforced concrete slabs. The damage index changes regularly with the distance of damages to the sensor. This relationship can be used to determine the damage location. The newly proposed damage index Ry/Rx is accurate in determining the damage location.

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The eigensolutions and associated eigensensitivities of an analytical model are usually calculated at the global structure level, which is time-consuming or even prohibitive for large-scale structures. Several substructuring approaches have been proposed that divide the global structure into some manageable substructures and assemble parts of the eigensolutions and eigensensitivities of the substructures to recover those of the global structure. However, these approaches are not usually accurate, as only the lowest eigensolutions and eigensensitivities are retained and the higher modes are excluded. In this paper, a new iterative substructuring method is proposed to accurately obtain the eigensolutions and eigensensitivities of structures. With this new approach, the contribution of the higher modes to the reduced eigenequation is retained as a residual flexibility matrix in an iterated form, which allows the eigenvalues and eigenvalue derivatives to be obtained from the previous results. The eigenvectors and their derivative matrices can be calculated from a reduced eigenequation directly without iteration. Upon convergence, the iterative scheme reproduces the eigensolutions and eigensensitivities of the original structure exactly. The computational efficiency and numerical accuracy of the proposed method are verified by the applications to a cantilever plate structure and an actual super-tall structure.

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