论文部分内容阅读
在结构修改和模型校正中．模态展开法是计算特征向量摄动量的常用方法之一，但当高阶模态被截断时．它会带来很大的截断误差．本文利用已知的有限阶模态，构造了Ｎ维欧氏空间的一个新基──混合基，并将特征向量的摄动量在新基上展开来计算特征向量的一、二阶摄动量．该方法使得不管截断模态个数的多少，其精度总与全模态展开法相同，且计算量都远少于全模态展开法，与改进的部分模态展开法相比．本方法不要求所截留的模态为连续的低阶模态，也能保证与全模态展开法相同的计算精度，这对于基于实验模态的修改意义更为重大，因为一方面实验模态难以测全，另一方面，在许多实验中很难保证所测得的各阶模态为连续的低阶模态，在这种情况下，现有的部分模态展开法根本无法实现．
In the structural changes and model calibration. The modal expansion method is one of the commonly used methods to calculate the perturbation of eigenvectors, however, when the higher modes are truncated. It will bring a lot of truncation error. In this paper, we use a known finite-order modal to construct a new basis-mixing matrix of N-dimensional Euclidean space and calculate the first and second order perturbation of the eigenvector by expanding the perturbation of the eigenvector on the new basis. The method makes the accuracy of the same modal expansion method the same as that of the full modal expansion method, regardless of the number of truncated modalities, and the computational load is far less than the full modal expansion method, compared with the improved partial mode unfolding method. The method does not require the retained mode to be a continuous low-order mode, and the same computational accuracy as the full-mode unfolding method can be guaranteed. This is even more significant for modal-based modification because, on the one hand, the experimental mode On the other hand, in many experiments, it is difficult to ensure that the measured modes are continuous low-order modes. In this case, the existing partial mode expansion method can not be realized at all.