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A hybrid finite element method (hybrid FEA) for computing mid-frequency vibrations for systems that contain one energy type is presented. In the mid-frequency range a system is comprised of both long and short members. Long members contain several wavelengths and they are modeled by the Energy Finite Element Analysis (EFEA). Short members contain a small number of wavelengths and they are modeled by the Finite Element Analysis (FEA). External excitation can be applied on long and/or on short members. Systems are analyzed by both the hybrid FEA method and an analytical solution in order to validate the hybrid FEA developments. The interaction among long and short members is defined by a set of equations between the EFEA and the FEA primary variables at the interfaces between long and short members. The numerical systems of equations for the long and the short members, and the interface equations are solved simultaneously.

The theoretical development of a hybrid finite element method is presented. It combines conventional Finite Element Analysis (FEA) with Energy Finite Element Analysis (EFEA) in order to achieve a numerical solution to mid-frequency vibrations. In the mid-frequency range a system is comprised by some members that contain several wavelengths and some members that contain a small number of wavelengths. 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. Since the work presented in this paper constitutes a fundamental step in the development of a hybrid method for mid-frequency analysis, the formulation for one flexural degree of freedom in co-linear beams is presented.