# Damage Detection Using Modal Rotational Mode Shapes Obtained with a Uniform Rate CSLDV Measurement
## 5 Conclusions  
In this paper, the damage detection method using the modal rotational mode shapes obtained from a uniform rate CSLDV technique is presented. The proposed Zigzag continuously scanning strategy is capable to acquire the mode shape data of the tested structure with any spatial resolution based on the mode shape demodulation method. This approach plays a paramount role in further damage detection. Without a priori knowledge of the undamaged structure, a polynomial function fitting method is proposed to reconstruct the ODS of undamaged state in order to meet the requirement to establish a damage indicator. In addition, a modal rotational damage indicator (RDI) is proposed and is used to detect and localize the cracks of a clamped plate structure. Investigations of a numerical simulation and experimental tests validated the proposed method. Results show that three cases with different cracks on the plate can be correctly identified using the experimental measurement data.  
The modal rotational mode shapes are much more sensitive to the structural damage detection than the displacement mode shapes because they are the first derivative of the detailed displacement mode shapes of transitional DOFs with respect to the orthogonal directions. However, its accuracy relies on the spatial resolution and noise contamination in the measurement. With the development of laser technique, the uniform rate CSLDV method can greatly improve the accuracy and spatial resolution of the mode shape measurement. If the very low scan frequency is selected, the rotational damage indicator may clearly identify the local anomaly features caused by the slight damage. Therefore, damage detection based on the modal rotational mode shapes can be widely used in practice. The CSLDV techniques make damage detection effective and efficient, especially for ultra-light structures or structures with composite materials due to the features of the noncontact and full field measurement. In addition, any uncertainties in the measurement may affect the damage detection. For example, high temperatures will produce heat radiation on the surface of the structure and therefore introduce measurement noise when using CSLDV. Thus, the effect of noise on the damage detection must be eliminated before the damage detection technique is applied. Such work is underway and the results will be reported in the future. In another way, the change of boundary conditions will affect the dynamics of the structure but have little effect on the damage detection indicator since the proposed method is only based on the measurement of the damaged structure. The mode shape of the undamaged structure is obtained by polynomial function fitting using the measured mode shape data of the damaged state. This is one advantage of the proposed method.  
Conceptualization and Methodology, Z.H. and C.Z.; Numerical Analysis and Experimental validation, Z.H.; writing--original draft preparation, Z.H.; writing--review and editing, C.Z.  
This research was funded by the National Natural Science Foundation of China and National Safety Academic Foundation of China, grant number U1730129.  
The authors gratefully appreciate the supports from Jiangsu Province Key Laboratory of Aerospace Power System, the Key Laboratory of Aero-engine Thermal Environment and Structure, Ministry of Industry and Information Technology are also gratefully acknowledged.  
The authors declare no conflict of interest.  
Figure 14: The RDI colored plot of the slight crack plate with the scanning rates of 0.05 Hz at the x direction and 10 Hz at the y direction. (**a**) The first torsion mode of 233.43 Hz. (**b**) The second torsion mode of 750.94 Hz.