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传统的模型缩阶及模态扩阶方法是以计算传递矩阵为手段。该文提出一种实测模态振型空间不完备问题的直接处理方法,即未测试自由度振型值的直接估计方法。通过引入一复合向量,该向量由对应于主自由度的实测振型值与对应于从自由度的待估算值组成。依靠实测模态及有限元模型信息对复合向量中未测试自由度的振型值进行重新估算,进而获得空间完备的模态振型。该文采用5自由度的弹簧-质量体系验证方法的正确性;借助平面框架结构探讨新方法较传统方法在低阶模态振型估算精度上的优势。数值结果表明:所提出方法不需质量归一化条件以及实测模态与有限元振型的比例条件;同时,该方法较传统方法在低阶模态振型扩阶上具有更好的精度,并允许有限元模型具有一定的模型误差。
Traditional model reduction and modal expansion method is to calculate the transfer matrix as a means. In this paper, a direct method to deal with the problem of incomplete modal vibration modes is proposed, ie, a direct estimation method for the unmodel vibration mode values. By introducing a complex vector consisting of the measured mode shapes corresponding to the main degrees of freedom and the values to be estimated corresponding to the degrees of freedom. Relying on the measured modal and finite element model information to re-estimate the unmodified vibration modes in the composite vector, and then get the complete modal shape. In this paper, we use the 5-DOF spring-mass system to verify the correctness of the method. The plane frame structure is used to explore the advantages of the new method in the accuracy of low-order mode shape estimation compared with the traditional method. The numerical results show that the proposed method does not require the mass normalization conditions and the ratio conditions of the measured modes and the finite element mode shapes. Meanwhile, the proposed method has better accuracy than the traditional method at low- And allow the finite element model has a certain model error.