This study aims to analyze the free vibrations of the Euler-Bernoulli beam vibrating in the vicinity of an inviscid, irrotational, and incompressible fluid, as well as Winkler soil, using the differential transformation method. To show the robustness of the proposed formulation, it is used in different numerical tests in which the free vibration of different soil-beam-fluid systems is assessed. The differences between these systems are rooted in their supports and the soil characteristics. Furthermore, the results achieved from the proposed method are compared with those of the finite element strategy. It is emphasized that the differential transformation method employed in this study showcases sufficient precision and reliability throughout the analysis process.

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