A method of detecting the location of damage in shear structures by using only the changes in first two natural frequencies of the translational modes is proposed. This damage detection method can determine the damage location in a shear building by using a Damage Location Index (DLI) based on two natural frequencies for undamaged and damaged states. In this study, damage is assumed to be represented by the reduction in stiffness. This stiffness reduction results in a change in natural frequencies. The uncertainty associated with system identification methods for obtaining natural frequencies is also carefully considered. Some simulations and experiments on shear structures were conducted to verify the performance of the proposed method. 1. Introduction In the structural health monitoring (SHM) field, many damage detection algorithms based on the modal properties of a structure, such as modal frequencies, mode shapes, curvature mode shapes, and modal flexibilities, have been studied for several decades. However, with most algorithms, identifying the precise location and magnitude of the damage is difficult. If not completely impossible, the accuracy and reliability are not sufficient [1]. Zhao and DeWolf [2] presented a sensitivity study comparing the use of natural frequencies, mode shapes, and modal flexibilities for monitoring. Based on the fact that natural frequencies are sensitive indicators of structural integrity, the relationship between frequency changes and structural damage was discussed in a review by Salawu [3]. Many of the methods using changes in natural frequencies to detect damage were summarized by Doebling in [4]. The amount of literature is large, comprising not only applications to various structures, but also theoretical work on the use of frequency shifts for damage detection. Besides, the trade-off relation between the number of sensors and the damage detection accuracy should be considered when installing the SHM system. A large number of sensors results in a high system cost as well as the need for enormous effort for wiring and installation. Complicated and expensive SHM systems are not feasible for most buildings [5]. Some methods have performed well at frequency-based damage identification for a few degrees of freedom. For larger engineering structures, the number of natural frequencies that can be identified is smaller than the number of structural elements. This is one of the reasons why frequency change methods have limited damage detection abilities [6]. To overcome these problems, some researchers have been using the
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