Keywords: beam, framework, finite element method, dynamic stiffness method, Wittrick-Williams algorithm, shape function.

The accuracy and reliability of the finite element method (FEM) in free vibration analysis of beams and frameworks are assessed by the dynamic stiffness method (DSM). When applying FEM, individual beams and frameworks are modelled by using a progressively increasing number of elements. The accuracy and convergence of results are then judged against exact results using DSM. The limitation of FEM in which free vibration analysis cannot be carried out beyond the order of the mass and stiffness matrices, and the loss of accuracy in computing higher natural frequencies, are highlighted. The investigation has shown that in the low and medium frequency range, FEM is reliable, but in the high frequency range, FEM can become inaccurate and unreliable. Evaluation of modal analysis using FEM in the high frequency range is important, particularly for the statistical energy analysis method, because the modal density of structures in the high frequency range is usually high. Furthermore, the need for accurate and reliable high frequency vibration analysis for beams and frameworks is important in energy flow analysis. It is in this context that the assessment of FEM in free vibration analysis of beams and frameworks is expected to be most effective and useful.

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