A hybrid finite element–energy finite element method for mid-frequency vibrations of built-up structures under multi-distributed loadings

In this study, a hybrid method combining finite element analysis and energy finite element analysis is developed to predict the vibrations of built-up structures in mid-frequency, and the associated general formulations are derived. The interactions between the structural components are modeled using a global matrix of the system and the reverberant blocked force. To validate the proposed method, three examples of different built-up structural systems, subjected to different types of excitations, are analyzed and discussed. These types of excitations are single point, multipoint and distributed forces on stiff member or flexible member. The results predicted by the presented method show good agreements with the dense finite element model, and the detailed local energies of the whole system are acquired under the different regional loadings. These results indicate that the proposed method can be utilized for the prediction of vibrations in the mid-frequency range.