Free vibration analysis of sandwich beams using dynamic finite element (DFE) and FEM formulations

The Dynamic Finite Element (DFE) theory is employed to calculate the natural frequencies and mode shapes of three-layered sandwich beams. Three formulations are developed and tested using a  number of different numerical cases. The first two theories pertain to the analysis of straight beams while the third one is developed for the analysis of curved beams. The results from all three derivations agree well with published data that uses Classical Finite Element (FEM) theory and the Dynamic Stiffness Method (DSM) in the analysis of the free vibration behaviour of sandwich beams. For all test cases, the DFE results agree well with the published results as well as the FEM developed as an additional benchmark for the DFE. The results of the research are very encouraging and demonstrate that DFE is a  valuable structural analysis tool that can be used in conjunction with FEM and DSM.