With the rapid development of a continuously scanning laser Doppler vibrometer (CSLDV) technique, the full-field mode shapes of structures with high accuracy can be obtained. In this paper, a novel damage detection method using modal rotational mode shapes obtained with a uniform rate CSLDV measurement is proposed. The modal rotational damage indicators considering the changes of modal rotational mode shapes between the damaged and the undamaged states are established. Because the modal rotational mode shapes are obtained through the derivative of the detailed displacement mode shapes of transitional degree-of-freedoms (DOFs) with respect to the orthogonal directions, they are more sensitive than the normal displacement mode shapes. The uniform rate CSLDV measurement is essentially a uniform straight-line scanning technique and the measured mode shapes can be directly obtained through the demodulation of vibration signals. Besides, taking it for granted that a priori knowledge of the undamaged structure is not known, the undamaged mode shapes can be reconstructed from the measured damaged data using the fitted polynomial functions in which the minimum number of polynomial function coefficients are determined by a fit value threshold. The proposed method is firstly demonstrated by numerical simulation of the crack plate and then a plate structure with three damaged cases is taken as an example for further experimental study. The experimental results indicate the following: (1) The uniform rate CSLDV measurement can obtain the high accuracy modal rotational mode shapes with the advantage of eliminating the contaminated noise in the measurement; (2) the modal rotational damage indicators of the torsional modes are the most sensitive to the crack damage and they can clearly identify single, multiple damages and locations of the plate, and even slight crack damage, respectively. The effectiveness of the method paves the way for practical applications, such as ultra-light or composite structures.
Rotational degrees of freedom (DOF) are usually indirectly derived from the measured translational DOF in structural dynamic tests by using the finite difference method. However, the noise of translational DOF measurement is easily propagated and further amplified when the finite difference method is employed to obtain the rotational DOF. Therefore, the accuracy of the obtained rotational DOF was rather poor. In order to overcome this disadvantage, a novel approach of using a dual sinusoidal-scan continuously scanning laser Doppler vibrometer (CSLDV) with the objective of obtaining the structural modal rotational DOFs is put forward in this paper. For plate structures, the operational deformation shape of the normal translational DOFs can be measured and described with polynomial functions through the modulation of CSLDV output signals. Then, rotational out-of-plane DOFs can be achieved with respect to the first derivatives of the polynomial functions along orthogonal directions. In such a way, the measurement noise that considerably affects the rotational out-of-plane DOFs derived from normal translational DOF can be significantly eliminated. The approach is validated experimentally with a cantilever plate structure, and a comparison with the results obtained from discrete point measurement is given. The results demonstrate the noticeable improvement in accuracy and spatial resolution of the proposed technique.
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