Dynamic finite modeling for local structure using dynamic condensation

Vibration fatigue is usually induced by local resonant of a structure where the excessive vibration occurred within a local region of the structure. In order to minimize the computation scale of dynamic response in vibration fatigue analysis, it is necessary to build the dynamic finite element model of the local structure. A dynamic finite element modeling method based on the strategy of "separation with dynamic equivalence" was proposed. In this method, the idea of dynamic condensation was applied to separate the local structure from the global structure. And the elastic and inertial effects of the surrounding structure on the local structure were considered by using an equivalent stiffness matrix and an equivalent mass matrix. The global structure was firstly meshed by a coarse fmite element grid. The global vibration characteristics were calculated. Then the separated local structure was meshed by a refined grid to build a finite element model for the local structure. The coordinate locating matrix for the surrounding structure was established. The local structure modes with the refined grid are obtained by interpolation from the local structure modes with the coarse grid. Together with the modes of surrounding structure, the dynamic condensation matrix was constructed. Then the dynamic equivalent stiffness and mass matrices were obtained through matrix transform which could be directly incorporated into the refined finite element model of the local structure. Compared with the finite element model of the global structure, the refined model has a lower order with high precision for the calculation of dynamic response. Numerical examples were also presented to verif' the feasibility and accuracy of this method.