A hybrid finite element method for computing mid-frequency vibrations is presented. In the mid-frequency region a system is comprised by some members that contain several wavelengths and some members that contain a small number of wavelengths within their dimensions. The former are considered long members and they are modeled by the Energy Finite Element Analysis (EFEA). The latter are considered short and they are modeled by the Finite Element Analysis (FEA). In this paper the excitation is considered to be applied on the short members. The hybrid formulation computes the response of the entire system. The characteristics of the long members affect the behavior of the short members and the amount of power flow between the members of the system. The resonant characteristics of the short members and the boundary conditions imposed by the long members determine the amount of input power into the system. The interaction between members is described by a set of equations between the FEA and the EFEA primary variables at the interfaces between long and short members. The equations for the short and the long members and the interface equations are solved simultaneously. A theoretical formulation and a numerical implementation for systems that contain one wave type is presented. Analytical solutions for several co-linear beam configurations are compared to numerical results produced by the hybrid finite element method. Good correlation is observed for all analyses.

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