Basic Development of Hybrid Finite Element Method for Midfrequency Structural Vibrations

The theoretical development of a hybrid finite element method is presented. It combines conventional finite element analysis (FEA) with energy FEA (EFEA) to achieve a numerical solution to midfrequency vibrations. In the midfrequency range a system comprises some members that contain several wavelengths and some members with just a few wavelengths within their lengths. The former are considered long members, and they are modeled by the EFEA. The latter are considered short, and they are modeled by the FEA. The new formulation is based on deriving appropriate interface conditions at the joints between sections modeled by the EFEA and the FEA methods. The formulation for one flexural degree of freedom in colinear beams is presented in this fundamental development. The excitation is considered to be applied on a long member, and the response of the entire system is computed. Uncertainty effects are imposed only on the long members of the system. Validation cases for several configurations are presented. They compare closed-form analytical solutions to numerical results produced by the hybrid finite element method. Good correlation is observed for all analyses. The resonant behavior of the short members is captured correctly in the response of the system.

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