对称结构模态振型的Zernike矩描述方法

摘要

Vibration mode shape description of a symmetrical structure using Zernike moment descriptor (ZMD) is introduced in this paper. The structural mode shapes can be decomposed as a line combination of a series of Zernike polynomials, with the feature of each Zernike polynomial reflecting a part of characteristic of mode shapes, based on Zernike moment transformation. The procedure to determine the number of Zernike polynomials for mode shape description is suggested. Meanwhile, the reconstruction of mode shapes with Zernike moment descriptor is carried out and its ability to filter the noise contaminated in the mode shapes is studied. The advantage of using Zernike moment descriptor to depict the mode shapes of a symmetric structure is verified by simulation with a disk structure as an example. The result demonstrates that the Zernike moment description of the mode shapes can be effectively describe the double modes in the symmetric structure and such a description has the ability to remove or significantly reduce the influence of noise in the mode shapes. Such feature shows a great practical value for further research on Finite Element model updating and validation of symmetric structures.%讨论了利用Zernike矩描述对称结构模态振型的方法,通过对结构的模态振型数据进行Zernike矩变换,将其分解成一系列Zernike矩的线性组合,而每一个Zernike矩反映模态振型的一部分形状特征.不同特征矩的线性组合,可以代表各阶模态的振型.在此基础上进一步提出了确定Zernike多项式最高阶数的方法,并讨论了Zernike矩描述对称结构模态振型的方法及其去噪声的能力.通过对简单圆盘结构的仿真实例研究,验证了应用Zernike矩描述对称结构模态振型的优越性.结果表明；利用Zernike矩描述对称结构的模态振型可以更有效地描述对称结构的模态,包括重模态,同时还能有效地消除测试数据中噪声的影响,对进一步实现对称结构有限元模型修正和模型确认具有重要的应用价值.