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本文基于模态矢量的正交性准则,定义了一新型的模态参数——互易性模态矢量。根据定义,互易性模态矢量正交于在给定频率范围内的模态矢量。互易性模态矢量是从频响函数、相对应的模态矢量和复数特征值(模态频率和阻尼系数)推导而得。由于它的推导与别的模态矢量无关,这些矢量的点积能用于透彻了解模态矢量的正交性关系,而这种理论上成立的正交关系可能在模态识别过程中被破坏。本文提出两种互易性模态矢量的计算方法(直接最小二乘法和递推最小二乘法)。还讨论了正交性检查以后模态矢量的质量改进。最后,为说明所提出的理论,给出了数位和试验的实例。
Based on the orthogonality criterion of modal vector, this paper defines a new type of modal parameter - reciprocity modal vector. By definition, reciprocity modal vectors are orthogonal to modal vectors over a given frequency range. The reciprocity modal vector is derived from the frequency response function, the corresponding modal vector, and the complex eigenvalues (modal frequencies and damping coefficients). Since its derivation has nothing to do with other modal vectors, the dot product of these vectors can be used to thoroughly understand the orthogonality of modal vectors, and this theoretical orthogonality may be destroyed in the modal recognition process . In this paper, we propose two methods of computing reciprocity modal vectors (direct least squares and recursive least squares). We also discuss the quality improvement of modal vectors after orthogonality checking. Finally, to illustrate the proposed theory, examples of digits and experiments are given.