As a result of environmental and accidental actions, damage occurs in structures. The early detection of any defect can be achieved by regular inspection and condition assessment. In this way, the safety and reliability of structures can be increased. This paper is devoted to proposing a new and effective method for detecting, locating, and quantifying beam-like structures. This method is based on the RayleighRitz approach and requires a few numbers of natural frequencies and mode shapes associated with the undamaged and damaged states of the structure. The great advantage of the proposed approach against the other methods is that it considers all kinds of boundary and damping effects. To detect damage using the penalty method, this article considers lumped rotational and translational springs for determining the boundary conditions. The results indicate that the proposed method is an effective and reliable tool for damage detection, localization, and quantification in the beam-like structures with different boundary conditions even when the modal data are contaminated by noise.

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