A hybrid finite element formulation for mid-frequency analysis of systems with excitation applied on short members

A hybrid finite element method for computing mid-frequency vibrations is pr esented. In the mid-frequency region a system is comprised by some members that contain several wavelengths and some members that contain a small numb er of wavelengths within their dimensions. The former are considered long m embers and they are modelled by the energy finite element analysis (EFEA). The latter are considered short and they are modelled by the finite element analysis (FEA). In this paper the excitation is considered to be applied o n the short members. The hybrid formulation computes the response of the en tire 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 e quations between the FEA and the EFEA primary variables at the interfaces b etween long and short members. The equations for the short and the long mem bers and the interface equations are solved simultaneously. A theoretical f ormulation and a numerical implementation for systems that contain one wave type is presented. Analytical solutions for several co-linear beam configu rations are compared to numerical results produced by the hybrid finite ele ment method. Good correlation is observed for all analyses. (C) 2000 Academ ic Press.