STRUCTURAL RESPONSE RECONSTRUCTION BASED ON MODE SYNTHESIS METHOD AND MODAL SUPERPOSITION METHOD IN THE PRESENCE OF CLOSELY SPACED MODES

A structural response reconstruction methodology based on mode synthesis method and modal superposition method in the presence of closely spaced modes is proposed. The whole structure is condensed into a super element model with fewer degrees of freedom through two coordinate transformations, and then the modes of the super element model are divided into closely spaced mode and residual mode. The single order residual mode response of the known response is separated by empirical mode decomposition method, and then the residual mode response of the position to be measured is reconstructed. The closely spaced mode response of the position to be measured can be calculated from the mode shape and the residual mode. The time-domain response reconstruction under the closely spaced mode is realized by mode superposition method. Numerical simulation studies were carried out to verify the accuracy and efficiency of the proposed method by comparing the theoretical response values of the measured position with the reconstructed values. In addition, the influences of the number of main modes, number of substructures, measurement noise and damping on the reconstructed results were studied in detail. The results show that this method greatly reduces the amount of reconstructed data through model condensation and overcomes the deficiency of the traditional EMD method which cannot separate the modes with small frequency interval, and thus cannot realize response reconstruction. Whether there are closely spaced modes or not, it can be applied to the reconstruction of structural stress, strain, displacement, acceleration and other dynamic responses.