A basic development of a hybrid finite element method for mid -frequency computations of structural vibrations.

Abstract

The frequency spectrum for structural vibration analysis can be divided into three regions: low, mid, and high frequency. In the mid-frequency range some members of a system have low modal density (short members) and other members present high modal density (long members). The conventional Finite Element Analysis (FEA) is a practical simulation tool for low frequency vibrations. The Energy Finite Element Analysis (EFEA) is a viable method for simulating high frequency vibrations. Neither FEA nor EFEA works well in the mid-frequency range due to high computational cost or inaccurate predictions, respectively. In this thesis an innovative and fundamentally new hybrid finite element method is developed for computing mid-frequency vibrations of systems that contain one type of energy. In the hybrid FEA long members are modeled by the EFEA and short members 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, and solving simultaneously the systems of FEA equations, EFEA equations, and the compatibility equations at the joints. The excitation is considered to be applied on long or short members or on both, and the response of the entire system is computed. Validation cases for several configurations of co-linear beams are presented. Analytical solutions and numerical results produced by the hybrid finite element method are compared. Good correlation is observed in all applications. The resonant behavior of the short members is captured correctly in the response of the system.