基于模态综合法和模态叠加法的密集模态结构响应重构

提出一种基于模态综合法和模态叠加法的密集模态结构响应重构方法，通过两次坐标变换将全结构缩聚为自由度更少的超单元模型，将超单元模型的模态分为密集模态和剩余模态。通过经验模态分解法分离出已知响应中单阶的剩余模态响应，进而重构出待测位置的剩余模态响应，待测位置的密集模态响应可由模态振型和剩余模态计算得到，通过模态叠加法实现在密集模态下的时域响应重构。进行了数值模拟研究，将待测位置响应的理论值与重构值进行比较以验证该方法的精度和效率，此外还详细研究了主模态数量、子结构划分方式、测量噪声和阻尼对重构结果的影响。结果表明：该文方法通过模型缩聚大大减少了重构的数据量，并且改善了传统EMD方法不能分离频率间隔较小的模态而无法实现响应重构这一不足，无论密集模态存在与否都可适用于结构的应力、应变、位移、加速度等多种动力响应的重构。

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.