# A Study on the Feasibility of Natural Frequency-Based Crack Detection
## 7 Future Work  
The findings in this study may help further explore the scope of the application of natural frequency-based crack detection. To extend the current methodology to more general structures or applications, the following aspects merit consideration. Although crack-induced natural frequency changes can be difficult to measure, it is still possible to amplify the frequency change. For example, in the active vibration control study by [PERSON] and [PERSON] [49], piezoelectric sensor and actuator patches are attached to cantilevered composite plates with internal flaws. The natural frequency of the damaged plate is found to increase by 1.11% to 5.13% because of the vibration suppression effect from the control piezo. This concept can be utilized conversely to adjust the local stiffness covered by piezoelectric patches, thereby amplifying the natural frequency changes induced by cracks [50]. Enhancing natural frequency measurements. As explained in Appendix D, 0.1 Hz has been considered the threshold for measurable frequency change in this study to represent a common situation after referring to typical experimental studies. However, more accurate frequency measurement is still possible, for example, in low frequency ranges [34; 35], using embedded fibre-optic Bragg gratings [51], and using piezoelectric sensors [52; 53]. To overcome the limitations of traditional sensors due to complex wiring, the design and application of passive wireless sensors have been investigated, such as passive radio frequency identification (RFID) sensors [54; 55; 56]. The development of such smart sensors enables real-time monitoring of natural frequency changes with high accuracy, which significantly enhances the effectiveness of natural frequency-based crack detection. Coping with environmental factors. The current study excludes environmental factors such as temperature fluctuations, humidity, and operational loads that may affect natural frequency measurements and mask the effects of small cracks. To handle environmental factors, a number of approaches may be considered such as temperature compensation algorithms accounting for temperature-induced changes [57], filtering environmental noise using advanced signal processing techniques [58], and multi-sensor scheme mitigating uncertainties [59]. Predicting critical crack length for general structures. To utilize the solution of \(K\) directly, this study focuses exclusively on cracks lying along the centerline. However, in practical scenarios, cracks may exhibit varying lengths, angles, and locations. For general structures with arbitrary crack configurations, the methodology illustrated in Figure 2 remains applicable. Nevertheless, when an analytical solution for \(K\) is unavailable, the \(J\)-integral [25; 26] serves as a more suitable parameter for characterizing unstable crack growth or failure. The analytical solution of the \(J\)-integral is available for certain simple structures [60; 61]. When the structure being investigated is complex, the \(J\)-integral can be calculated using the XFEM. Similarly, changes in natural frequency can be evaluated using the FEM. Considering a breathing crack. In practical applications, cracks may exhibit a breathing behaviour where the crack surfaces intermittently open and close under dynamic loading or environmental conditions. In the current study, if a breathing crack were considered, the solution of \(K\) would remain applicable; however, a breathing crack typically causes smaller changes in natural frequencies compared to fully open cracks of the same size [62]. The natural frequency calculation would become more challenging due to the bilinear dynamic behaviour [63] of the cracked plate. It would be valuable to investigate whether the conclusions drawn in this study remain valid under these conditions. For example, entropy as a measure to quantify the bilinearity of the vibration response caused by a breathing crack has been investigated recently [64; 65]. Internet of Things (IoT) and big data solutions.