In vibration-based damage detection problems, sensitivity-based techniques are applicable and robust approaches for detecting and identifying damage in civil and mechanical engineering systems. A salient characteristic of a well-established sensitivity function is its ability to detect damage by itself without using any mathematical solution methods. This article, therefore, presents a novel modal sensitivity function based on a combination of fundamental dynamic equations. The proposed sensitivity function is associated with the mode shape that is established by combining the eigenvalue problem and orthogonality conditions. The main contribution of the proposed function is its sensitivity to damage and applying a few dynamic and physical characteristics for formulating the sensitivity matrix. A high compatibility with incomplete modal parameters is another innovation of the proposed sensitivity function that makes it as an applicable approach for using in vibration-based applications. To demonstrate the accuracy and capability of the proposed sensitivity function, the numerical model of the ASCE SHM benchmark structure is applied. Results show that the proposed function has a reliable sensitivity to damage and can detect damage without solving the damage equation by any mathematical solution methods.

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