Application of the dynamic condensation approach to the hybrid FE-SEA model of mid-frequency vibration in complex built-up systems

The hybrid Finite Element (FE) – Statistical Energy Analysis (SEA) method developed for mid-frequency vibration of complex built-up systems needs to compute the total dynamic flexibility matrix at every frequency, which is very time consuming. This paper presents an improved hybrid FE-SEA method to overcome this problem. In the present method, first, dynamic condensation is introduced to reduce the order of the deterministic FE component, which results in significant reduction of the total dynamic stiffness matrix. Then, noting that the dynamic stiffness matrix of the deterministic component is established by using the FE method, a fast inverse algorithm is employed to calculate the dynamic flexibility matrix of the slave degrees of freedom of the deterministic component generated in the condensation process. These two steps avoid the direct inverse computation of a large matrix at each frequency point of interest, resulting in significant time saving. A numerical example illustrates the efficiency and convergence of the proposed method.