Coupling of Finite Element and Energy Finite Element Solutions for Calculating the Vibration of Co-linear Beams in the Mid-Frequency Range

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. 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.