Vibration-based damage detection is a range of methods that utilizes the dynamic response of a structure to evaluate its condition and detect damage. It is an important approach for structural health monitoring and has drawn much attention from researchers. While multiple reviews have been published focusing on different aspects of this field, there has not been a study specifically examining the recent development across the range of methods, including natural frequency, mode shape, modal curvature, modal strain energy, and modal flexibility-based damage detection methods. This paper aims to fill this gap by reviewing the recent application of these methods in civil structures, including beams, plates, trusses, frames, and composite structural members. The merits and limitations of each method are discussed, and research opportunities are presented. This broader review also provides an opportunity for critical comparison across this range of methods. While predominantly reviewing experiment-based studies, this review also considers some numerical studies that may motivate further research.

Owing to the long-standing statement that natural frequency-based crack detection is not sensitive enough to localised damage to identify small cracks, many natural frequency-based crack detection methods are validated by detecting cracks of moderate size. However, a direct comparison between the crack severity causing a measurable natural frequency change and the crack severity reaching the initiation of crack propagation or leading to brittle fracture is constantly ignored. Without this understanding, it is debatable whether the presented crack detection methods are feasible in practical situations. Through natural frequency calculation and linear elastic fracture mechanics, this study is dedicated to filling the above gap in knowledge. To directly utilize the solution of stress intensity factor, common fracture toughness test specimens featuring a single-edge crack are used. These specimens are essentially cracked rectangular plates under uniform uniaxial tension. Considering the stress resultants obtained via the extended finite element method, the natural frequency of the loaded cracked plates is calculated using the Rayleigh–Ritz method incorporating corner functions. In addition, assuming the specimens as structural components under remote uniform tension, the development of critical load versus crack length is derived based on the solution of the stress intensity factor. Thus, critical crack lengths corresponding to a series of safety factors are obtained by equating service load with critical load. After obtaining natural frequencies of the cracked plates with critical crack lengths, the natural frequency drop caused by a critical crack can be computed. Hence, the critical crack length can be compared with the crack length when the frequency drop is measurable. It is found that the brittleness of the employed metals plays a vital role in the feasibility of natural frequency-based crack detection.

This study presents an approximate method for determining the natural frequency of a system composed of a beam and a two-degree-of-freedom spring-mass system. The expression for estimating the natural frequency is derived following the standard procedures of the forced vibration analysis of a beam. The results obtained using the current method are in good agreement with those obtained through the dynamic stiffness method, especially when the spring stiffness is large. The innovativeness of the current method is that it reveals the relevance between the natural frequency of the system, the natural frequency of the beam, and the mode shape data at the positions where the spring-mass system is attached to the beam. The method is potentially useful in the dynamic wheel-track interaction analysis because the train wheel is normally simplified as a spring-mass system with high spring stiffness. It may also be applied to natural frequency-based damage detection where an auxiliary spring-mass system is used. When the spring-mass system roves on the beam, the curve of natural frequency versus spring-mass system location would be relevant to the mode shape square which is sensitive to local damage.