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在结构模态识别中常用的模态保证准则(MAC)仅能显示结构不同振型的相关性,并不能反映模态的细节,对于模态复杂的网壳结构则更是如此。因此,提出利用Zernike矩表征网壳结构的振型,即将振型数据视为图像函数,通过离散Zernike矩变换,得到表征各阶模态的Zernike矩值(包括幅值和相位角)。对一个单层球面网壳结构的有限元模型进行数值模拟,结果表明,此矩可有效地反映模态的振型特性并能识别结构的重频模态,较传统的MAC具有明显的优越性。在此基础上,初步提出将Zernike矩的幅值及相位角作为结构损伤识别的新指标。构造了网壳结构杆件物理参数改变的几种损伤工况,通过分析,发现了不同的损伤形式导致的Zernike矩的不同变化规律,验证了Zernike矩用于损伤识别的可行性。
The modal guarantee criterion (MAC), which is commonly used in structural modal recognition, can only show the correlation between different modes of structures and can not reflect the details of modes. This is even more so for the mode-reticulated shell structure. Therefore, it is proposed that the Zernike moment can be used to characterize the mode of the reticulated shell structure. That is to say, the mode shapes are regarded as image functions. The Zernike moments (including amplitude and phase angle) characterizing each mode are obtained by discrete Zernike moment transformation. The numerical simulation of the finite element model of a single-layer spherical reticulated shell shows that the moment can effectively reflect the mode shape characteristics of the mode and can recognize the structure’s repetition mode, which is obviously superior to the traditional MAC . On this basis, the amplitude and phase angle of Zernike moment are proposed as a new index of structural damage identification. Several damage conditions of physical and mechanical parameters of reticulated shell structure were constructed. Through analysis, the different variation rules of Zernike moments caused by different damage forms were found, and the feasibility of Zernike moments for damage identification was verified.