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This paper presents two approaches to modelling the vibrations of three-layer beams with asymmetric faces. Two sets of differential equations of motion for such composite are derived. Despite sharing a common displacement hypothesis, they differ significantly. The first is based on fundamental equilibrium conditions that must be satisfied at every beam cross-section (EE). The second is the result of applying a variational approach (VAR) and minimizing the composite’s energy in a global scale. In the presented computational example, both models are used to investigate the free vibration frequencies of a specific set of layered beams, and the obtained results are compared with FEM results. It should be emphasized that FEM models do not require any a priori assumed deformation hypothesis. Consequently, the presented calculations demonstrate not only the correctness and applicability of the presented modelling approaches but also the usefulness of the assumed hypothesis. The presented analysis shows that both the EE and VAR systems of motion are applicable to vibration analysis of sandwich beams in a wide range of typical design cases. As ‘typical’ composites one should consider asymmetric sandwich beams with relatively thin faces, where the core thickness is at least 25 times greater than thickness of any outer layers, and with any ratio of material properties of all layers. In less typical design cases, where the faces of the composite are only 10 times thinner than its core, the presented analytical solutions are still applicable to vibration analysis, but they may generate higher relative errors when compared to FEM. Based on the presented results, assessing such ‘unusual’ composites using VAR is not recommended. In such case the EE approach results should be considered as more predictable and closer to those obtained with FEM.
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