# A Study on the Feasibility of Natural Frequency-Based Crack Detection
## 1 Introduction  
Structural Health Monitoring (SHM) is the process of identifying and characterising structural damage and assessing structural safety status. It is an active area of research, with appreciable technical potential and wide applications in the aerospace industry, automotive systems, mechanical systems and civil structures. Among multiple approaches to SHM, methods based on the measurement of structural dynamic signatures (i.e., vibration-based damage detection methods) are in continuous development. Vibration-based methods offer a non-destructive and economical means to identify cracks. Amidst a wide range of vibration-based methods such as natural frequency [1], mode shape [2], modal curvature [3], modal strain energy [4], modal flexibility-based methods [5], etc., natural frequency-based crack detection methods are considered efficacious and cost-efficient by many researchers and are thus investigated in this study. The presence of a crack tends to reduce structural stiffness and hence decrease natural frequencies to varying extents that largely depend on the crack location and severity. Therefore, the natural frequency shift induced by a crack has been used in crack detection [6, 7]. However, the relative frequency change caused by small areas of damage may be difficult to measure unless the natural frequency of high modes is also examined. For this reason, common crack detection methodologies [8; 9; 10; 11; 12; 13; 14; 15; 16] use cracks of moderate size in their work. For a crack with a normalized severity (i.e., normalized crack length or normalized crack depth) of 10% or below, the magnitude of natural frequency change tends to be small, especially for the first two modes, posing a challenge to the natural frequency measurement if environmental effects are also considered [17; 18; 19; 20; 21]. It would be difficult to distinguish between a small natural frequency change and measurement noise. Consequently, for the validation of various crack detection methods, the commonly used normalized crack severity is above 10%. However, when the normalized crack severity reaches 10% or higher, whether the structure is safe enough to remain in service is questionable. This means the potential use of these methods for early detection of cracks is also questionable. The phenomenon that a small crack only induces minor frequency change in low modes is not confined to beam-like or plate-like structures, but is also observed in crack detection studies for other engineering applications such as hydraulic structures [22], swept wings [23], and rotor systems [24]. This raises an important question: Can a crack be detected by natural frequency measurement at an early stage before it compromises structural integrity? The work presented here addresses this question. Taking the frequency change as input data, the performance of crack detection methods can be tested. While the concept that natural frequency changes due to cracks may be demonstrated, the feasibility of these methods for practical applications remains to be investigated. To assess the feasibility, it would require the comparison between the crack severity causing a measurable frequency change and the crack severity reaching the start of crack growth. Therefore, it is necessary to address the question: \"Between the measurable natural frequency change and the onset of crack growth, which one happens earlier?\" Investigation into this question appears to be lacking in the literature. This is possibly because, on the one hand, natural frequency-based crack detection and unstable crack propagation are problems of two different categories. The former employs modal parameters (in this case, the natural frequency) to identify changes in physical properties (e.g., mass, damping, and stiffness) caused by a crack, while the latter is analysed using fracture mechanics.